不含4-,5-圈且无相交3-面的平面图的星边染色

Star Edge-coloring of Plane Graphs Without 4-,5-Cycles and Intersecting 3-Faces

图G的星边染色是指G的一个正常边染色满足G中无长为4的路(或圈)是2-边染色的.使得图G有星边染色的最小颜色数k称为G的星边色数,记为χ′st(G).证明了若平面图G不含4-5-圈且无相交3-面,则χ′st(G)≤[1.5Δ]+10.

A star edge-coloring of a graph G is a proper edge coloring without 2-colored paths(or cycles)of length 4.The smallest k for which G admits a star edge-coloring with k colors is called the star chromatic index,denoted byχ′st(G).In this paper,it is proved that if G is a plane graph without 4-,5-cycles and intersecting 3-faces,thenχ′st(G)≤[1.5Δ]+10.