List Edge Coloring of Outer-1-planar Graphs
Copyright policy )List Edge Coloring of Outer-1-planar Graphs
A graph is outer-1-planar if it can be drawn in the plane so that all vertices are on the outer face and each edge is crossed at most once. It is known that the list edge chromatic number $χ'_l(G)$ of any outer-1-planar graph $G$ with maximum degree $Δ(G)\geq 5$ is exactly its maximum degree. In this paper, we prove $χ'_l(G)=Δ(G)$ for outer-1-planar graphs $G$ with $Δ(G)=4$ and with the crossing distance being at least 3.
21 pages, 4 figures
- Xidian University China (People's Republic of)
outerplanar graph, FOS: Computer and information sciences, Coloring of graphs and hypergraphs, Discrete Mathematics (cs.DM), outer-1-planar graph, 05C15, 05C10, FOS: Mathematics, Mathematics - Combinatorics, crossing distance, Combinatorics (math.CO), list edge coloring, Planar graphs; geometric and topological aspects of graph theory, Computer Science - Discrete Mathematics
outerplanar graph, FOS: Computer and information sciences, Coloring of graphs and hypergraphs, Discrete Mathematics (cs.DM), outer-1-planar graph, 05C15, 05C10, FOS: Mathematics, Mathematics - Combinatorics, crossing distance, Combinatorics (math.CO), list edge coloring, Planar graphs; geometric and topological aspects of graph theory, Computer Science - Discrete Mathematics
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