Books Published

with B. Bollobas, Extremal Graph Theory, in "Graph Theory", CRC Press, 2003 

Energy of matrices and norms of graphs, in Energies of Graphs -- Theory and Applications, I. Gutman, X. Li (Eds.), Mathematical chemistry monographs 17, University of Kragujevac and Faculty of Science, Kragujevac, 2016, pp. 5--48.

Refereed Journal Publications

with M. Tait and C. Timmons, Degenerate Turán problems for hereditary properties, Electron. J. Combin. 25 (2018), Paper 4.39

with O. Rojo, On the $alpha$-index of graphs with pendent paths, Linear Algebra Appl. 550 (2018), 87--104.

Merging the A- and Q-spectral theories, Applicable Anal. and Discr. Math. 11 (2017), 81–107

The spectral radius of graphs with no K2,t minor, Linear Algebra Appl. 531 (2017), 510–515

Combinatorial methods for the spectral p-norm of hypermatrices, Linear Algebra Appl. 529 (2017), 324–354

with N. Agudelo,  On the minimum trace norm/energy of (0,1)-matrices, Linear Algebra Appl. 526 (2017) 42–59.

with G. Pastén, O. Rojo, and R.L. Soto,  On the A_alpha-spectra of trees,  Linear Algebra Appl. 520 (2017) 286-305.

with O. Rojo, A note on the positive semidefinitness of A_alpha, Linear Algebra Appl. 519 (2017), 156–163.

Hypergraphs and hypermatrices with symmetric spectrum, Linear Algebra Appl. 519 (2017), 1–18

Remarks on the energy of regular graphs, Linear Algebra Appl. 508 (2016), 133–145.

Spectral radius and Hamiltonicity of graphs with large minimum degree, Czech. Math. J. 66 (2016), 925–940.

Beyond graph energy: norms of graphs and matrices, Linear Algebra Appl. 506 (2016), 82–138.

Max k-cut and the smallest eigenvalue, Linear Algebra Appl. 504 (2016), 462–467.

with L. de Lima and C. Oliveira, The clique number and the smallest Q-eigenvalue of graphs, Disc. Math. 339 (2016), 1744–1752.

with M.A.A. de Freitas and L. Patuzzi, Maxima of the Q-index: graphs with no K_{s,t}, Linear Algebra Appl. 496 (2016), 381–391.

with C. M. da Silva Jr, Graph functions maximized on a path, Linear Algebra Appl. 485 (2015), 21–32.

Extrema of graph eigenvalues, Linear Algebra Appl. 482 (2015), 158–190

The trace norm of r-partite graphs and matrices, C. R. Math. Acad. Sci. Paris, Ser. I 353 (2015), 471–475

with L.Y. Kang and X.Y. Yuan, The p-spectral radius of k-partite and k-chromatic uniform hypergraphs, Linear Algebra Appl. 478 (2015), 81–107

with X.Y. Yuan, Maxima of the Q-index: Forbidden even cycles, Linear Algebra Appl. 471 (2015), 636–653 

with X.Y. Yuan, More eigenvalue problems of Nordhaus-Gaddum type, Linear Algebra Appl. 451 (2014), 231-245.

with X.Y. Yuan, Maxima of the Q-index: graphs without long paths, Electronic J. Linear Algebra 27 (2014), 504-514.

L.Y. Kang and V. Nikiforov, Extremal problems for the p-spectral radius of graphs, Electronic J. Combin. 21 (2014), P3.21.

with  M.A.A. de Freitas and L. Patuzzi, Maxima of the Q-index: forbidden 4-cycle and 5-cycle, Electronic J. Linear Algebra 26 (2013), 905-916

Analytic methods for uniform hypergraphs, Linear Algebra Appl. 457 (2014), 455--535.

Some extremal problems for hereditary properties of graphs, Electronic J. Combin. 21 (2014), P1.17.

Maxima of the Q-index: degenerate graphs, Electronic J. Linear Algebra 27 (2014), 250-257.

An asymptotically tight bound on the Q-index of graphs with forbidden cycles, Publ. Inst. Math. (Beograd) (N.S.) 95(109) (2014), 189-199.

with X. Yuan, Maximum norms of graphs and matrices, and their complements, Linear Algebra Appl. 439, (2013), 1538--1549.

The influence of Miroslav Fiedler on spectral graph theory, Linear Algebra Appl. 439 (2013), 818-821. 

with N.M.M. de Abreu, Maxima of the Q-index: Graphs with bounded clique number, Electronic J. Linear Algebra 24 (2013), 121-130.

with L.S de Lima, On the second largest eigenvalue of the signless Laplacian, Linear Algebra Appl. 438 (2013), 1215-1222. 

with B. Bollobás, Degree Powers in Graphs: The Erdõs-Stone Theorem, Combin. Probab. Comp. 21 (2012), 89-105.  

with N.M.M. de Abreu, Maxima of the Q-index: abstract graph properties,  Electronic J. Linear Algebra 23 (2012), 782-789.  

Some new results in extremal graph theory, in Surveys in Combinatorics 2011 (ed. R. Chapman), LMS Lecture Note Series 392, Cambridge University Press 2011, pp. 141-183.   

with L.S. de Lima, C.S. Oliveira, N.M.M. de Abreu, The smallest eigenvalue of the signless Laplacian, Linear Algebra Appl. 435 (2011), 2570-2584  

On the sum of k largest singular values of graphs and matrices, Linear Algebra Appl. 435  (2011) 2394-2401    

Extremal norms of graphs and matrices, J. Math Sci. (2012), 164-174. 

with H. Li and R.H. Schelp, A new type of Ramsey-Turan problems, Discrete Math. 310 (2010) 3579-3583    

with B. Bollobas, Large joints in graphs, Eur. J. Combinatorics 32 (2011) 33-44        

The number of cliques in graphs of given order and size, Transactions of AMS 363 (2011) 1599-1618 

with B. Bollobas, The number of graphs with large forbidden subgraphs, Eur. J. Combinatorics 31 (2010) 1964-1968       

Spectral saturation: inverting the spectral Turan theorem, Electronic J. Combin. 15 (2009), R33.   

 A spectral Erdos-Stone-Bollobas theorem, Combin. Probab. Comput. 18 (2009), 455-458.   

Complete r-partite subgraphs of dense r-graphs, Discrete Math. 309 (2009), 4326-4331.  

The spectral radius of graphs without paths and cycles of specified length, Linear Algebra Appl.  432 (2010), pp. 2243-2256.

with M. Fiedler, Spectral radius and Hamiltonicity of graphs, Linear Algebra Appl. 432 (2010), 2170-2173.

Degree powers in graphs with forbidden even cycle, Electronic J. Combin. 15 (2009), R107. 

A contribution to the Zarankiewicz problem,  Linear Algebra Appl. 432 (2010), 1405-1411.

Turan's theorem inverted, Discrete Math. 310 (2010), 125-131.    

 Stability for large forbidden subgraphs, J. Graph Theory 62 (2009), 362-368.   

The maximum spectral radius of C4-free graphs of given order and size, Linear Algebra Appl. 430 (2009), 2898-2905. 

 More spectral bounds on the clique and independence numbers, J. Combin. Theory Ser. B 99  (2009), 819-826. 

with C.C. Rousseau, Ramsey Goodness and Beyond, Combinatorica.  29 (2009), 227-262.   

Graphs with many copies of a given subgraph, Electron. J. Combin. 15 (2008), N6.     

with B. Bollobas, An Abstract Regularity Lemma, in Building Bridges, Grotschel, Katona eds. Bolyai Soc. Math. Studies, 19, Springer, 2008.    

The energy of C4-free graphs of bounded degree, to appear in Linear Algebra Appl. 428 (2008), 2569-2573.  

The spectral radius of subgraphs of regular graphs, Electronic J. Combin. 14 (2007), N20.   

A spectral condition for odd cycles, to appear in Linear Algebra Appl. 428 (2008), 1492-1498.  

with B. Bollobas, Graphs and Hermitian matrices: exact interlacing, Discrete Math. 308 (2008), 4816-4821. 

Graphs with many r-cliques have large complete r-partite subgraphs, Bull. London Math. Soc. 40 (2008), 23-25.  

Bounds on graph eigenvalues II, Linear Algebra Appl. 427 (2007) 183-189.   

with R.H. Schelp, Cycles and Stability, J. Combin. Theory Ser. B 98 (2008), 69–84.   

Chromatic number and spectral radius, Linear Algebra Appl. 426 (2007), 810-814.   

Numerical radius and zero pattern of matrices, J. Math. Anal. Appl. 337 (2008) 739–743.     

with B. Bollobas, Joints in graphs, Discrete Math. 308 (2008), 9-19. 

The sum of the squares of degrees: sharp asymptotics, Discrete Math. 307 (2007), 3187-3193.  

with B. Bollobas, Cliques and the Spectral Radius, J. Combin. Theory Ser. B. 97 (2007), 859-865.   

Revisiting two classical results on graph spectra, Electronic J. Combin. 14 (2007), R14.   

Linear combinations of graph eigenvalues, Electron. J. Linear Algebra 15 (2006), 329-336.  

Eigenvalues and forbidden subgraphs I, Linear Algebra Appl. 422 (2007), 384-390. 

Eigenvalues and extremal degrees in graphs, Linear Algebra Appl. 419 (2006), 735-738.  

The Energy of Graphs and Matrices, J. Math. Anal. Appl. 326 (2007), 1472-1475. 

Graphs and Matrices with Maximal Energy, J. Math. Anal. Appl. 327 (2007), 735-738.  

with S. M. Cioaba and D. Gregory, Extreme eigenvalues of nonregular graphs, J. Combin. Theory Ser. B. 97 (2007), 483-486. 

with R.H. Schelp, Making the components of a graph k-connected, Discrete Appl. Math. 155 (2007) 410-415. 

Bounds on graph eigenvalues I,  Linear Algebra Appl. 420 (2007), 667-671.  

Eigenvalue problems of Nordhaus-Gaddum type,  Discrete Math. 307 (2007), 774-780. 

The smallest eigenvalue of K_r-free graphs, Discrete Math. 306 (2006), 612-616. 

with R.H. Schelp, Cycle lengths in graphs with large minimum degree, J. Graph Theory 52 (2006), 157-170.   

with B. Bollobas, Degree sums in cliques, Electronic J. Comb. 12 (2005), #N21.  

Walks and the spectral radius of graphs, Linear Algebra Appl. 418 (2006), 257-268.  

Eigenvalues and degree deviation in graphs, Linear Algebra and Appl. 414 (2006) 347-360.     

Edge distribution of graphs with few induced copies of a given graph, Combin. Probab. Comp. 15 (2006), 895-902. 

with C.C. Rousseau and R.H. Schelp, Book Ramsey numbers and quasi-randomness, Combin. Probab. Comp. 14 (2005), 851-860.   

with B. Bollobas, Degree powers in graphs with forbidden subgraphs, Electronic J. Comb. 11 (2004), R47.   

with C. C. Rousseau, Book Ramsey numbers I, Random Struct. Alg. 27 (2005), 379-400.    

with B. Bollobas, Graphs and Hermitian matrices: eigenvalue interlacing, Discrete Math. 289 (2004), 119-127.   

with C. C. Rousseau, A note for Ramsey numbers for books,  J. Graph Theory  49 (2005), 168-176.    

with B. Bollobas, Graphs and Hermitian matrices: discrepancy and singular values, Discrete Math. 285 (2004), 17-32.     

The cycle-complete graph Ramsey numbers,   Combin. Probab. Comp. 14 (2005), 349-370.      

with B. Bollobas, Books in graphs, Eur. J. Combin 26 (2004), 259-270.      

with C. C. Rousseau, Large generalized books are p-good, J. Combin. Theory Ser B 92 (2004), 85-97.    

with R.H. Schelp, Cycles and paths in graphs with large minimum degree, J. Graph Theory 47 (2004), 39-52.         

with E. Gyori and R.H. Schelp, Nearly bipartite graphs, Discrete Math. 272 (2003), 187-196.        

Some inequalities for the largest eigenvalue of a graph, Combin. Probab. Comp. 11 (2002), 179--189.   

On the edge distribution of a graph, Combin. Probab. Comp. 10 (2001), 543—555.   

On the minimum number of k-cliques in graphs with restricted independence number, Combin. Probab. Comp. 10 (2001), 361--366.    

with N. Khadziivanov, (in Russian),  On the theorems of Borsuk-Ulam and Ljusternik-Shnirel’man-Borsuk, Ann. Univ. Sofia, Liv. 1 84 (1990), 83-89.  

with N. Khadziivanov, (in Russian), A solution of a problem of Erdos on the maximum number of triangles with a common edge in a graph, C. R. Acad. Sci. Bul. 34 (1981), 969-970.    

with N. Khadziivanov, (in Russian), A solution of a problem of Erdos on the maximum number of triangles in a graph with n vertices and [sq(n)/4]+l edges, C. R. Acad. Sci. Bul. 32 (1979), 1315-1318.    

with N. Khadziivanov, (in Russian), An upper bound on the number of cliques in graphs with restricted independence number, Serdica 5 (1979), 50-59.   

with S. Stefanov, (in Russian), A generalization of the Borsuk-Ulam theorem, Math. and Educ. in Math., Proc. 8th Spring Conf. UBM, 1979, 423-427.  

with N. Khadziivanov, (in Russian), On the inequality of Nordhaus-Stewart-Moon-Moser, Serdica 4 (1978), 344-350.   

with N. Khadziivanov, (in Russian), An upper bound on the number of triangles in a graph, Math. and Educ. in Math., Proc. 7th Spring Conf. UBM, 1978, 541-543.  

with N. Khadziivanov, (in Russian), On the theorem of Borsuk-Ulam, Math. and Educ. in Math., Proc. 6th Spring Conf. UBM, 1977, 135-137.  

On a problem of Erdos, (in Bulgarian), Ann. Univ. Sofia, 71 (1976/77), Part II, 157-160.    

Presentations - Conference (refereed *)

Spectral norms and spectral radius of hypergraphs, invited talk, ILAS conference 2019

The spectral norm and spectral radius of hypermatrices, plenary talk, West Canada Linear Algebra Meeting 2018

The maximum p-spectral radius of hypergraphs of given size, plenary talk, International Workshop on Spectral Hypergraph Theory, 2017, Hefei, PR China

The p-spectral radius and the spectral p-norm of hypergraphs and hypermatrices
EXCILL III: Extremal Combinatorics at Illinois, Chicago, August 2016

Merging the A-  and Q-spectral theories
XXV Congreso de Matemáticas Capricornio, Antofagasta, Chile, August 2016

Plenary talk
Hypergraphs and hypermatrices with symmetric spectrum
XXV Congreso de Matemáticas Capricornio, Antofagasta, Chile,  August 2016

Extrema of graph eigenvalues
AMS Spring Southeastern Sectional Meeting University of Georgia, March 2016, Athens, GA

Spectral methods for extremal problems in hypergraphs
Universidade Federal do Rio de Janeiro, Mar. 2014

Asymptotic Ramsey numbers for books, Tongji University,
Shanghai, Nov., 2013

Spectral bounds for k-degenerate graphs, East China Normal University Shanghai, Nov. 2013

Spectral extremal problems for hypergraphs, Mighty Conference, April, 2013, Miami University  

Spectral problems of Nordhaus-Gaddum type,  AMS Spring Southeastern Sectional Meeting, University of Mississippi, Oxford, Mississippi, 2013 

Asymptotic Ramsey numbers of books, EXCILL2 Conference, 2013, University of Illinois Urbana-Champaign  

An Erdos-Stone Theorem for Hypergraphs, SIAM meeting, Halifax, 2012. 

The influence of Miroslav Fiedler on spectral graph theory, ILAS conference 2011, Braunschweig, Germany  

Some new results in extremal graph theory, GTCA Conference, July, 2011, Beijing  

Some new results in extremal graph theory,  23 British Combinatorial Conference 2011, Exeter, UK    

Extremal norms of graphs and matrices, Summer meeting of CMS 2011, University of Alberta, Edmonton, Canada 

The sum of the k largest singular values of graphs and matrices, CANADAM 2011  

Extremal graph Theory and the signless Laplacian, Atlanta Lecture Series in Combinatorics and Graph Theory II, Atlanta, February 2011   

Extremal graph theory and the signless Laplacian, Banff, February 2011   

Cut norms and spectra of matrices, ILAS 2010 conference in Pisa, Italy

How can we investigate very large networks, SPOLM 2010, Rio de Janeiro, Brazil  

Hereditary matrix properties, Banff, January 2010  

Almost all small induced subgraphs of a graph are spectrally similar to it,  Algebraic Graph Theory Workshop, Worcester, MA, April, 2009 

The spectra of hereditary graph properties, AMS 2009 Meeting, Worcester, MA 

The number of cliques of given order and size, AMS-MAA-SIAM 2009 Meeting, Washington, DC 

 New bounds in the Zarankiewicz problem, AMS 2009 Meeting, Urbana, IL  

The spectral radius of graphs with forbidden sparse subgraphs, SGT-in-Rio 2008, Rio de Janeiro

The spectral radius of C4-free graphs, AMS 2008 sectional meeting, Bloomington Indiana

Building extremal graph theory on spectral grounds, Geometric and Algebraic Combinatorics, Oisterwijk, Netherlands, 2008    

An extension of the Erdos-Stone theorem, AMS 2007 Meeting, DePaul University, Chicago 

Powers of the degrees of graphs, Combinatorics Seminar, University of Memphis, 2006  

Inversion and stability in Turan type extremal problems: case studies and applications, SIAM conference on Discrete Mathematics, 2006, Victoria, Canada.   

Inversion and stability in Turan and Ramsey type problems, “Random Graphs and Large-Scale Real-World Networks” workshop, 2006, National University of Singapore.     

Cycles lengths in graphs with large minimum degree, Invited talk at the International conference on graph structure theory in Wuhan, China, 2005. Presenter R. Schelp

The structure of graphs with few induced copies of a given graph,  Erdos Conference, Memphis, 2005;     

Graphs and Hermitian matrices: eigenvalues and discrepancy,  FIM Workshop, ETH Zurich 2004;     

Cycle-complete graph Ramsey number, Erdos Conference, Memphis, 2003;     

Presentations - Universities/Industry (refereed *)

Spectral bounds for k-degenerate graphs, Jiao Tong University, Shanghai, Oct. 2013

Extremal problems for sums of powers of degrees, Lanzhou University, July, 2011, Lanzhou, China   

Some new results in extremal graph theory, Shanghai Jiaotong University, July, 2011  

Some new results in extremal graph theory, Xi'an Jiaotong University, China, July, 2011    

Cut-norms and spectra of matrices, Georgia Tech Institute, April 2010   

The number of cliques of given order and size, Georgia State University, April 2010     

Cut-norm, cut-distance and the operator norm of matrices, Combinatorics seminar, University of Memphis, 2009  

Some combinatorial contributions to analysis, Combinatorics Seminar, University of Memphis, 2008   

New results in classical and modern extremal problems, Combinatorics Seminar, University of Memphis, 2007    

Extremal Graph Theory via Spectra, Discrete Math Seminar, University of Delaware, Apr 13, 2007    

The energy of graphs, Institute for Mathematical Sciences, National University of Singapore, 2006      

Other Presentations (refereed *)

 The number of cliques of given order and size,  22 Cumberland Conference, WKU, Bowling Green, KY, 2009  

Conditions where the graphs is almost bipartite, 15^th Cumberland Conference on Combinatorics, Graph Theory, and  Computing, Oxford, Mississippi, 2002. Presenter R. Schelp;  

Appendix A

Appendix B

Appendix C

Appendix D

Appendix E