4 papers · 1 filter
The Proof of the Alon--Kim Conjecture
Chengshuo Qiao, Zhijun Lu, Huimin Song
In 1997, Alon and Kim proposed an asymptotic edge-coloring bound motivated by a bound on the number of edges in intersecting uniform hypergraphs. The Alon--Kim conjecture asserts t…
-Avoiding Coloring and B-Coloring under Bipartite Exclusions
Zhijun Lu, Qirui Ying, Huimin Song
Let be a nonempty family of connected bipartite graphs, each with at least two edges. For a graph , a proper vertex coloring of is -avoiding i…
Proper conflict-free choosability of sparse graphs with girth at least seven
Xingqin Qi, Huimin Song, Zhulou Cao
A proper conflict-free coloring of a graph is a proper vertex coloring in which every non-isolated vertex has a color appearing exactly once in its neighborhood. A graph is pro…
Proper Conflict-Free Choosability for Graphs with Bounded Average Degree
Zhijun Lu, Qirui Ying, Huimin Song
For a graph , a proper coloring of is called proper conflict-free if for every non-isolated vertex , there is at least one color appearing exactly once in . A gra…