Crossing-critical graphs with large maximum degree

Details Crossing-critical graphs with large maximum degree Crossing-critical graphs with large maximum degree

2009-07-09

arxiv.org/abs/0907.1599v1

J. Combin. Theory, Ser. B 100 (2010) 413-417

Mathematics

Combinatorics

Scientific paper

10.1016/j.jctb.2009.11.003

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 of Richter is that their maximum degree is bounded in terms of $k$. In this note we disprove these conjectures for every $k\ge 171$, by providing examples of $k$-crossing-critical graphs with arbitrarily large maximum degree.

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