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The existence of biregular spanning subgraphs in bipartite graphs via spectral radius
Dandan Fan, Xiaofeng Gu, Huiqiu Lin
Biregular bipartite graphs have been proven to have similar edge distributions to random bipartite graphs and thus have nice pseudorandomness and expansion properties. Thus it is q…
Spectral expansion properties of pseudorandom bipartite graphs
Dandan Fan, Xiaofeng Gu, Huiqiu Lin
An -biregular bipartite graph is a bipartite graph with bipartition such that each vertex in has degree and each vertex in has degree . By the bipart…
Eigenvalues and factors: a survey
Dandan Fan, Huiqiu Lin, Hongliang Lu +1
A factor of a graph is a spanning subgraph satisfying some given conditions. An earlier survey of factors can be traced back to the Akiyama and Kano [J. Graph Theory, 1985, 9: 1-42…
Toughness and spectral radius in graphs
Yuanyuan Chen, Dandan Fan, Huiqiu Lin
The Brouwer's toughness conjecture states that every -regular connected graph always has where is the second largest absolute eigenvalue of the adjacency…
l-connectivity, l-edge-connectivity and spectral radius of graphs
Dandan Fan, Xiaofeng Gu, Huiqiu Lin
Let G be a connected graph. The toughness of G is defined as t(G)=min{\frac{|S|}{c(G-S)}}, in which the minimum is taken over all proper subsets S\subset V(G) such that c(G-S)\geq…
Spectral conditions for -extendability and -factors of bipartite graphs
Dandan Fan, Huiqiu Lin
Let be a connected graph. If contains a matching of size , and every matching of size is contained in a perfect matching of , then is said to be \emph{-ext…