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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…
Long cycles and spectral radii in planar graphs
Ping Xu, Huiqiu Lin, Longfei Fang
There is a rich history of studying the existence of cycles in planar graphs. The famous Tutte theorem on the Hamilton cycle states that every 4-connected planar graph contains a H…
A unified approach to the spectral radius, connectivity and edge-connectivity of graphs
Yu Wang, Dan Li, Huiqiu Lin
For two integers and , the \emph{-extra -component connectivity} of a graph is defined to be the minimum size of a subset of vertices whose…
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…
Extremal eigenvalues with respect to graph minors
Mingqing Zhai, Longfei Fang, Huiqiu Lin
Let denote the maximum spectral radius of -vertex -minor free graphs. The problem on determining this extremal value can be dated back to the early 1990s.…
On the spectral extremal problem of planar graphs
Xiaolong Wang, Xueyi Huang, Huiqiu Lin
The spectral extremal problem of planar graphs has aroused a lot of interest over the past three decades. In 1991, Boots and Royle [Geogr. Anal. 23(3) (1991) 276--282] (and Cao and…
Spectral extremal results on trees
Longfei Fang, Huiqiu Lin, Jinlong Shu +1
Let be the maximum spectral radius over all -free graphs of order , and be the family of -free graphs of order with spectral radius…