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M-degrees of quadrangle-free planar graphs
2009
Journal of Graph Theory
The M-degree of an edge xy in a graph is the maximum of the degrees of x and y. The M-degree of a graph G is the minimum over M-degrees of its edges. In order to get upper bounds on the game chromatic number, He et al showed that every planar graph G without leaves and 4cycles has M-degree at most 8 and gave an example of such a graph with M-degree 3. This yields upper bounds on the game chromatic number of C 4 -free planar graphs. We determine the maximum possible M-degrees for planar,
doi:10.1002/jgt.20346
fatcat:xhwcvuwdwjfwla25pbzdujiaka