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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