The Spectral Radii of Intersecting Uniform Hypergraphs

Berge, C.: Graphs and Hypergraphs, vol. 6, 2nd edn. North-Holland Mathematical Library, North-Holland Publishing Co., Amsterdam; London (1976)

Bretto, A.: Hypergraph Theory: an Introduction. Springer, Berlin (2013)

Bai, S.L., Lu, L.Y.: A bound on the spectral radius of hypergraphs with $$e$$ edges. Linear Algebra Appl. 549, 203–218 (2018)

Bu, C.J., Zhang, X., Zhou, J., Wang, W.Z., Wei, Y.M.: The inverse, rank and product of tensors. Linear Algebra Appl. 446, 269–280 (2014)

Chen, D.M., Chen, Z.B., Zhang, X.D.: Spectral radius of uniform hypergraphs and degree sequences. Front. Math. China 12, 1279–1288 (2017)

Cooper, J., Dutle, A.: Spectra of uniform hypergraphs. Linear Algebra Appl. 436, 3268–3292 (2012)

Chang, K.C., Pearson, K., Zhang, T.: Perron–Frobenius theorem for nonnegative tensors. Commun. Math. Sci. 6, 507–520 (2008)

Chang, K.C., Qi, L.Q., Zhang, T.: A survey on the spectral theory of nonnegative tensors. Numer. Linear Algebra Appl. 20, 891–912 (2013)

Erdős, P., Ko, C., Rado, R.: Intersection theorems for systems of finite sets. Quart. J. Math. Oxford Ser. 12(2), 313–320 (1961)

Frankl, P.: Erdős–Ko–Rado theorem with conditions on the maximal degree. J. Combin. Theory Ser. A 46, 252–263 (1987)

Friedland, S., Gaubert, S., Han, L.: Perron–Frobenius theorem for nonnegative multilinear forms and extensions. Linear Algebra Appl. 438, 738–749 (2013)

Frankl, P., Han, J., Huang, H., Zhao, Y.: A degree version of the Hilton–Milner theorem. J. Combin. Theory Ser. A 155, 493–502 (2018)

Frankl, P., Tokushige, N.: A note on Huang–Zhao theorem on intersecting families with large minimum degree. Discrete Math. 340, 1098–1103 (2017)

Frankl, P., Tokushige, N.: Invitation to intersection problems for finite sets. J. Combin. Theory Ser. A 144, 157–211 (2016)

Fan, Y.Z., Tan, Y.Y., Peng, X.X., Liu, A.H.: Maximizing spectral radii of uniform hypergraphs with few edges. Discuss. Math. Graph Theory 36, 845–856 (2016)

Godsil, C., Meagher, K.: Erdős–Ko–Rado theorems: algebraic approaches. Cambridge Studies in Advanced Mathematics, vol. 149. Cambridge University Press, Cambridge (2016)

Guo, H.Y., Zhou, B.: On the α-spectral radius of uniform hypergraphs. Discuss. Math. Graph Theory 40, 559–575 (2020)  

Han, J., Kohayakawa, Y.: The maximum size of a non-trivial intersecting uniform family that is not a subfamily of the Hilton–Milner family. Proc. Am. Math. Soc. 145, 73–87 (2017)

Hilton, A.J.W., Milner, E.C.: Some intersection theorems for systems of finite sets. Quart. J. Math. Oxford Ser. 2(18), 369–384 (1967)

Hu, S.L., Qi, L.Q.: The Laplacian of a uniform hypergraph. J. Comb. Optim. 29, 331–366 (2015)

Hu, S.L., Qi, L.Q.: The eigenvectors associated with the zero eigenvalues of the Laplacian and signless Laplacian tensors of a uniform hypergraph. Discrete Appl. Math. 169, 140–151 (2014)

Hu, S.L., Qi, L.Q., Xie, J.S.: The largest Laplacian and signless Laplacian H-eigenvalues of a uniform hypergraph. Linear Algebra Appl. 469, 1–27 (2015)

Huang, H., Zhao, Y.N.: Degree versions of the Erdős–Ko–Rado theorem and Erdős hypergraph matching conjecture. J. Combin. Theory Ser. A 150, 233–247 (2017)

Keevash, P., Lenz, J., Mubayi, D.: Spectral extremal problems for hypergraphs. SIAM J. Discrete Math. 28, 1838–1854 (2014)

Lin, H.Y., Guo, H.Y., Zhou, B.: On the α-spectral radius of irregular uniform hypergraphs. Linear Multilinear Algebra 68, 265–277 (2020)

Lin, H.Y., Mo, B., Zhou, B., Weng, W.M.: Sharp bounds for ordinary and signless Laplacian spectral radii of uniform hypergraphs. Appl. Math. Comput. 285, 217–227 (2016)

Li, H.H., Shao, J.Y., Qi, L.Q.: The extremal spectral radii of k-uniform supertrees. J. Comb. Optim. 32, 741–764 (2016)

Nikiforov, V.: Merging the A- and Q-spectral theories. Appl. Anal. Discrete Math. 11, 81–107 (2017)

Qi, L.Q.: Eigenvalues of a real supersymmetric tensor. J. Symbolic Comput. 40, 1302–1324 (2005)

Qi, L.Q., Shao, J.Y., Wang, Q.: Regular uniform hypergraphs, s-cycles, s-paths and their largest Laplacian H-eigenvalues. Linear Algebra Appl. 443, 215–227 (2014)

Shao, J.Y.: A general product of tensors with applications. Linear Algebra Appl. 439, 2350–2366 (2013)

Xiao, P., Wang, L.G.: The maximum spectral radius of uniform hypergraphs with given number of pendant edges. Linear Multilinear Algebra 67, 1392–1403 (2019)

Xiao, P., Wang, L.G., Lu, Y.: The maximum spectral radii of uniform supertrees with given degree sequences. Linear Algebra Appl. 523, 33–45 (2017)

Yang, Y.N., Yang, Q.Z.: Further results for Perron–Frobenius theorem for nonnegative tensors. SIAM J. Matrix Anal. Appl. 31, 2517–2530 (2010)

Yuan, X.Y., Zhang, M., Lu, M.: Some upper bounds on the eigenvalues of uniform hypergraphs. Linear Algebra Appl. 484, 540–549 (2015)