Geodesic
Properties of Large 2-Crossing-Critical Graphs
Journal of Graph Algorithms and Applications, Tome 26 (2022) no. 1, pp. 111-147.

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A $c$-crossing-critical graph is one that has crossing number at least $c$ but each of its proper subgraphs has crossing number less than $c$. Recently, a set of explicit construction rules was identified by Bokal, Oporowski, Richter, and Salazar to generate all large $2$-crossing-critical graphs (i.e., all apart from a finite set of small sporadic graphs). They share the property of containing a generalized Wagner graph $V_{10}$ as a subdivision. In this paper, we study these graphs and establish their order, simple crossing number, edge cover number, clique number, maximum degree, chromatic number, chromatic index, and treewidth. We also show that the graphs are linear-time recognizable and that all our proofs lead to efficient algorithms for the above measures. Keywords. Crossing number, crossing-critical graph, chromatic number, chromatic index, treewidth.
DOI : 10.7155/jgaa.00585
Keywords: crossing number, crossing-critical graph, chromatic number, chromatic index, treewidth 
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     author = {Drago Bokal and Markus Chimani and Alexander Nover and J\"oran Schierbaum and Tobias Stolzmann and Mirko Wagner and Tilo Wiedera},
     title = {Properties of {Large} {2-Crossing-Critical} {Graphs}},
     journal = {Journal of Graph Algorithms and Applications},
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Drago Bokal; Markus Chimani; Alexander Nover; Jöran Schierbaum; Tobias Stolzmann; Mirko Wagner; Tilo Wiedera. Properties of Large 2-Crossing-Critical Graphs. Journal of Graph Algorithms and Applications, Tome 26 (2022) no. 1, pp. 111-147. doi : 10.7155/jgaa.00585. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00585/

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