Crossing-critical graphs with large maximum degree
نویسندگان
چکیده
منابع مشابه
Crossing-critical graphs with large maximum degree
A conjecture of Richter and Salazar about graphs that are critical for a fixed crossing number k is that they have bounded bandwidth. A weaker well-known conjecture is that their maximum degree is bounded in terms of k. In this note we disprove these conjectures for every k ≥ 171, by providing examples of k-crossing-critical graphs with arbitrarily large maximum degree. A graph is k-crossing-cr...
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iráň constructed infinite families of k-crossing-critical graphs for every k ≥ 3 and Kochol constructed such families of simple graphs for every k ≥ 2. Richter and Thomassen argued that, for any given k ≥ 1 and r ≥ 6, there are only finitely many simple k-crossingcritical graphs with minimum degree r. Salazar observed that the same argument implies such a conclusion for simple k-crossing-critic...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2010
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2009.11.003