AI 中文总结
研究不含钻石图、无爪立方图是否为\((1, 1, 2, 3)\)-填充可染色的问题，通过对图\(G\)的分析给出肯定答案，核心方法是对\(V(G)\)进行特定划分，主要贡献是解决了相关填充染色问题。
AI 中文摘要
图\(G\)的\((1, 1, 2, k)\)-填充染色是将\(V(G)\)划分为两个独立集、一个2-填充和一个\(k\)-填充。最近在一篇论文中提出问题：每个无爪立方图是否是\((1, 1, 2, 3)\)-填充可染色的。对于不含钻石图、无爪立方图\(G\)，本文给出了肯定答案。
英文摘要
A $(1, 1, 2, k)$-packing coloring of a graph $G$ is a partition of $V(G)$ into two independent sets, a 2-packing, and a $k$-packing. Recently, the question was posed in [A short proof that every claw-free cubic graph is (1, 1, 2, 2)-packing colorable, arXiv:2512.24001v1] as to whether every claw-free cubic graph is $(1, 1, 2, 3)$-packing colorable. We provide an answer in the affirmative in the case that $G$ is a diamond-free, claw-free cubic graph.
