论文标题
关于外平面图的恒星色索引的猜想的注释
A note on a conjecture of star chromatic index for outerplanar graphs
论文作者
论文摘要
图$ g $的星缘着色是$ g $的适当边缘着色，没有双重路径或长度为四个。 IT星色素索引，$χ_{st}^{'}（g），$ g $的$是$ g $的最低数字$ k $，其星缘颜色为$ k $ colors。在\ cite {lb}中， L. Bezegov $ \急性{a} $等。推测$χ_{st}^{'}（g）\ leq \ lfloor \ frac {3δ} {2} {2} {2} \ rfloor+1 $ $ g $是带有外在的图形， 最高度$δ\ geq 3. $在本文中，我们获得了$χ_{st}^{'}（g）\leqΔ+6 $当$ g $是直径为2或3的2个连接的外平面图，如果$ g $是$ g $。
A star edge coloring of a graph $G$ is a proper edge coloring of $G$ without bichromatic paths or cycles of length four. The it star chromatic index, $χ_{st}^{'} (G ),$ of $G$ is the minimum number $k$ for which $G$ has a star edge coloring by $k$ colors. In \cite{LB}, L. Bezegov$\acute{a}$ et al. conjectured that $χ_{st}^{'} (G )\leq \lfloor\frac{3Δ}{2}\rfloor+1$ when $G$ is an outerplanar graph with maximum degree $Δ\geq 3.$ In this paper we obtained that $χ_{st}^{'}(G) \leq Δ+6$ when $G$ is an 2-connected outerplanar graph with diameter 2 or 3. If $G$ is an 2-connected outerplanar graph with maximum degree 5, then $χ_{st}^{'}(G) \leq 9.$
