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arxiv: 0907.1599 · v1 · pith:GE2ADHN5new · submitted 2009-07-09 · 🧮 math.CO

Crossing-critical graphs with large maximum degree

classification 🧮 math.CO
keywords degreegraphsmaximumboundedconjecturecrossing-criticallargerichter
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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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