کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6423576 | 1342419 | 2011 | 4 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: NoteParity vertex coloring of outerplane graphs NoteParity vertex coloring of outerplane graphs](/preview/png/6423576.png)
A proper vertex coloring of a 2-connected plane graph G is a parity vertex coloring if for each face f and each color c, the total number of vertices of color c incident with f is odd or zero. The minimum number of colors used in such a coloring of G is denoted by Ïp(G).In this paper we prove that Ïp(G)â¤12 for every 2-connected outerplane graph G. We show that there is a 2-connected outerplane graph G such that Ïp(G)=10. If a 2-connected outerplane graph G is bipartite, then Ïp(G)â¤8, moreover, this bound is best possible.
⺠The parity chromatic number of any 2-connected outerplane graph is at most 12. ⺠There is a 2-connected outerplane graph with parity chromatic number 10. ⺠The parity chromatic number of any 2-connected bipartite outerplane graph is at most 8.
Journal: Discrete Mathematics - Volume 311, Issue 21, 6 November 2011, Pages 2570-2573