The edge colorings of $K_{5}$-minor free graphs
The edge colorings of $K_{5}$-minor free graphs
In 1965, Vizing proved that every planar graph $G$ with maximum degree $��\geq 8$ is edge $��$-colorable. It is also proved that every planar graph $G$ with maximum degree $��=7$ is edge $��$-colorable by Sanders and Zhao, independently by Zhang. In this paper, we extend the above results by showing that every $K_5$-minor free graph with maximum degree $��$ at least seven is edge $��$-colorable.
14 pages, 1 figure
- Shandong Women’s University China (People's Republic of)
- Lanzhou University China (People's Republic of)
- Shandong University China (People's Republic of)
Coloring of graphs and hypergraphs, tree-decomposition, chromatic index, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), edge coloring, \( K_5\)-minor free graph, Planar graphs; geometric and topological aspects of graph theory
Coloring of graphs and hypergraphs, tree-decomposition, chromatic index, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), edge coloring, \( K_5\)-minor free graph, Planar graphs; geometric and topological aspects of graph theory
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