M-degrees of quadrangle-free planar graphs
نویسندگان
چکیده
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 C4-free planar graphs. We determine the maximum possible M-degrees for Contract grant sponsor: RFBR; Contract grant numbers: 08-01-00673, 06-01-00694; Contract grant sponsor: NSF; Contract grant numbers: DMS-0400498, DMS0650784, DMS-0652306. Journal of Graph Theory © 2008 Wiley Periodicals, Inc. 80 M-DEGREES OF QUADRANGLE-FREE PLANAR GRAPHS 81 planar, projective-planar and toroidal graphs without leaves and 4-cycles. In particular, for planar and projective-planar graphs this maximum is 7. © 2008 Wiley Periodicals Inc. J Graph Theory 60: 80–85, 2009
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ورودعنوان ژورنال:
- Journal of Graph Theory
دوره 60 شماره
صفحات -
تاریخ انتشار 2009