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math.CO2026
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…
math.CO2026
-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…
math.CO2026
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…