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arXiv · 1309.1841

Graphs that do not contain a cycle with a node that has at least two neighbors on it

Pierre Aboulker·Marko Radovanović·Nicolas Trotignon·Kristina Vušković
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Abstract

We recall several known results about minimally 2-connected graphs, and show that they all follow from a decomposition theorem. Starting from an analogy with critically 2-connected graphs, we give structural characterizations of the classes of graphs that do not contain as a subgraph and as an induced subgraph, a cycle with a node that has at least two neighbors on the cycle. From these characterizations we get polynomial time recognition algorithms for these classes, as well as polynomial time algorithms for vertex-coloring and edge-coloring.

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Pierre Aboulker, Marko Radovanović, Nicolas Trotignon, Kristina Vušković. 2013-09-07. Graphs that do not contain a cycle with a node that has at least two neighbors on it. https://doi.org/10.1137/11084933x

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