Graphs that do not contain a cycle with a node that has at least two neighbors on it
Discrete Mathematics
2016-03-27 v1 Combinatorics
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.
Keywords
Cite
@article{arxiv.1309.1841,
title = {Graphs that do not contain a cycle with a node that has at least two neighbors on it},
author = {Pierre Aboulker and Marko Radovanović and Nicolas Trotignon and Kristina Vušković},
journal= {arXiv preprint arXiv:1309.1841},
year = {2016}
}