A graph G is said to be crossing-critical if $cr(G-e)< cr(G)$ for every edge e of G, where $cr(G)$ is the crossing number of G. Richter and Thomassen [Journal of Combinatorial Theory, Series B 58 (1993), 217-224] constructed an infinite family of 4-regular crossing-critical graphs with crossing number $3$. In this article, we present a new infinite family of 4-regular crossing-critical graphs.
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Ding et al. (2024) studied this question.
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