Efficient Vertex- and Edge-Coloring of Outerplanar Graphs
✍ Scribed by Proskurowski, Andrzej; Sysło, Maciej M.
- Book ID
- 118213025
- Publisher
- Society for Industrial and Applied Mathematics
- Year
- 1986
- Weight
- 780 KB
- Volume
- 7
- Category
- Article
- ISSN
- 0196-5212
- DOI
- 10.1137/0607016
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## Abstract We prove that a 2‐connected, outerplanar bipartite graph (respectively, outerplanar near‐triangulation) with a list of colors __L__ (__v__ ) for each vertex __v__ such that $|L(v)|\geq\min\{{\deg}(v),4\}$ (resp., $|L(v)|\geq{\min}\{{\deg}(v),5\}$) can be __L__‐list‐colored (except when
Certain problems involving the coloring the edges or vertices of infinite graphs are shown to be undecidable. In particular, let G and H be finite 3-connected graphs, or triangles. Then a doubly-periodic infinite graph F is constructed such that the following problem is undecidable: For a coloring o