论文标题
强颜色2型图：循环限制和部分着色
Strong coloring 2-regular graphs: Cycle restrictions and partial colorings
论文作者
论文摘要
令$ h $为$δ（h）\ leq 2 $的图表，让$ g $通过$ h $从$ h $中获取$ k_4 $的$ h $。我们证明，如果$ h $最多包含一个超过$ 3 $的奇数周期，或者$ h $最多包含$ 3 $三角形，则$χ（g）\ leq 4 $。这证明了此类图$ h $的强烈着色猜想。对于我们定理未涵盖的$δ= 2 $的图形$ h $，我们证明了对猜想的近似结果。
Let $H$ be a graph with $Δ(H) \leq 2$, and let $G$ be obtained from $H$ by gluing in vertex-disjoint copies of $K_4$. We prove that if $H$ contains at most one odd cycle of length exceeding $3$, or if $H$ contains at most $3$ triangles, then $χ(G) \leq 4$. This proves the Strong Coloring Conjecture for such graphs $H$. For graphs $H$ with $Δ=2$ that are not covered by our theorem, we prove an approximation result towards the conjecture.
