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9 papers · 2 filters
Antimagic Orientation of Forests
Songling Shan, Xiaowei Yu
An antimagic labeling of a digraph with vertices and arcs is a bijection from the set of arcs of to such that all oriented vertex-sums are pa…
The Core Conjecture of Hilton and Zhao II: a Proof
Yan Cao, Guantao Chen, Guangming Jing +1
A simple graph with maximum degree is overfull if . The core of , denoted , is the subgraph of induced by its vertices of degre…
Pseudo-multifan and Lollipop
Yan Cao, Guantao Chen, Guangming Jing +1
A simple graph with maximum degree is \emph{overfull} if . The \emph{core} of , denoted , is the subgraph of induced by its ver…
Hamiltonicity of 3-tough -free graphs
Andrew Hatfield, Elizabeth Grimm
Chvátal conjectured in 1973 the existence of some constant such that all -tough graphs with at least three vertices are hamiltonian. While the conjecture has been proven for…
The overfullness of graphs with small minimum degree and large maximum degree
Yan Cao, Guantao Chen, Guangming Jing +1
Given a simple graph , denote by , , and the maximum degree, the minimum degree, and the chromatic index of , respectively. We say is \emph{-critic…
Chromatic index of dense quasirandom graphs
Songling Shan
Let be a simple graph with maximum degree . A subgraph of is overfull if . Chetwynd and Hilton in 1985 conjectured that a gra…