Year: 2026
Type: preprint
Abstract: For a graph $G$, a proper edge coloring of $G$ is called a D-coloring if every diamond subgraph of $G$ is rainbow. Let $χ'_D(G)$ be the D-chromatic index of $G$, which is the smallest integer $k$ such that $G$ admits a D-coloring with $k$ colors. Let $Δ$ be the maximum degree of $G$. The only known Brooks-type upper bound on $χ'_D(G)$ is $\frac{9}{16}Δ^2 + \frac{1}{2}Δ$, given by a greedy coloring. In this paper, using a probabilistic method, we obtain the first improvement upon this upper bound by proving that $χ'_D(G) \le (1-c)\frac{9}{16}Δ^2$ for some $c > 0$ and sufficiently large $Δ$.
Source: arXiv (Cornell University)
Authors: Tian, Lin, Wang, Runze
Institutions: Middle Tennessee State University, Augustana College
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7207770528
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