A graph G is called (k, d)\*-choosable if, for every list assignment L satisfying [L(v)l = k for all v E V(G), there is an L-coloring of G such that each vertex of G has at most d neighbors colored with the same color as itself. In this note, we prove that every planar graph without 4-cycles and /-c
β¦ LIBER β¦
A note on list-coloring powers of graphs
β Scribed by Kosar, Nicholas; Petrickova, Sarka; Reiniger, Benjamin; Yeager, Elyse
- Book ID
- 124117997
- Publisher
- Elsevier Science
- Year
- 2014
- Tongue
- English
- Weight
- 401 KB
- Volume
- 332
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
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## Abstract We prove that a 2βconnected, outerplanar bipartite graph (respectively, outerplanar nearβtriangulation) 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__βlistβcolored (except when
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