Rongxing Xu

math.CO2025

Remarks on proper conflict-free degree-choosability of graphs with prescribed degeneracy

Masaki Kashima, Riste Škrekovski, Rongxing Xu

A proper coloring $ϕ$ of $G$ is called a proper conflict-free coloring of $G$ if for every non-isolated vertex $v$ of $G$ , there is a color $c$ such that $∣ ϕ^{- 1} (c) \cap N_{G} (v) ∣ = 1$ …

math.CO2025

Proof of a conjecture of Voss on bridges of longest cycles

Jie Ma, Rongxing Xu

Bridges are a classical concept in structural graph theory and play a fundamental role in the study of cycles. A conjecture of Voss from 1991 asserts that if disjoint bridges $B_1,…

math.CO2025

Proper conflict-free degree-choosability of outerplanar graphs

Masaki Kashima, Riste Škrekovski, Rongxing Xu

A proper coloring $ϕ$ of $G$ is called a proper conflict-free coloring of $G$ if for every non-isolated vertex $v$ of $G$ , there is a color $c$ such that $∣ ϕ^{- 1} (c) \cap N_{G} (v) ∣ = 1$ …