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Every fork-free graph is perfectly weight divisible
Feng Liu, Shuang Sun, Yan Wang +2
A graph is \emph{perfectly weight divisible} if, for every positive integral weight function on and every induced subgraph of with at least one edge, the vertex…
Optimal coloring of -free graphs with no short odd holes
Feng Liu, Shuang Sun, Yan Wang
A \emph{hole} is an induced cycle of length at least four, and an \emph{even hole} is a hole of even length. A \emph{cap} is obtained from a hole by adding a vertex adjacent to exa…
Edge-disjoint Hamilton cycles under a bipartite-hole condition
Yanan Hu, Chengli Li, Feng Liu
In 2017, McDiarmid and Yolov introduced the bipartite-hole-number and proved that forces a Hamilton cycle. They also gave a sufficient con…
Tight Bound for Nikiforov's Spectral Even-Cycle Conjecture
Peiru Kuang, Feng Liu, Shuang Sun +2
Nikiforov conjectured that, for every fixed and all sufficiently large , the unique -vertex -free graph with maximum adjacency spectral radius is $S^+_{n,k}…
On the structures of {diamond, bowtie}-free graphs that do not contain an induced subdivision of
Feng Liu, Shuang Sun, Yan Wang
A graph is -free if it contains no induced subdivision of . Lévêque et al. [\emph{J. Combin. Theory Ser. B} \textbf{102} (2012) 924--947] conjectured that all…
On the Borodin--Kostochka conjecture for graphs with large maximum degree
Feng Liu, Shuang Sun, Yan Wang +1
The Borodin--Kostochka conjecture states that every graph with maximum degree satisfies . In this paper, we verify this conjecture for…
Cycles and paths through vertices whose degrees are at least the bipartite-hole-number
Chengli Li, Feng Liu, Yurui Tang
The bipartite-hole-number of a graph , denoted by , is the minimum integer such that there exist positive integers and with , satisfyi…
Trisimplicial vertices in (fork, odd parachute)-free graphs
Kaiyang Lan, Feng Liu, Di Wu +1
An {\em odd hole} in a graph is an induced subgraph which is a cycle of odd length at least five. An {\em odd parachute} is a graph obtained from an odd hole by adding a new ed…
An Ore-type condition for hamiltonicity in graphs
Chengli Li, Feng Liu
The bipartite-hole-number of a graph , denoted as , is the minimum number such that there exist positive integers and with with the propert…
Constructions of minimally -tough regular graphs
Kun Cheng, Chengli Li, Feng Liu
A non-complete graph is said to be -tough if for every vertex cut of , the ratio of to the number of components of is at least . The toughness o…
Longest cycles and longest chordless cycles in -connected graphs
Yanan Hu, Chengli Li, Feng Liu
Thomassen's chord conjecture from 1976 states that every longest cycle in a -connected graph has a chord. The circumference and induced circumference of a graph $…
The minimum size and maximum diameter of an edge-pancyclic graph of a given order
Chengli Li, Feng Liu, Xingzhi Zhan
A -cycle in a graph is a cycle of length A graph of order is called edge-pancyclic if for every integer with every edge of lies in a -cycl…
Bound vertices of longest paths between two vertices in cubic graphs
Chengli Li, Feng Liu
Thomassen's chord conjecture from 1976 states that every longest cycle in a -connected graph has a chord. This is one of the most important unsolved problems in graph theory. Le…