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Graphs that do not contain a cycle with a node that has at least two
neighbors on it
release_pmfelha6qvac7fmrlkmrvfoowi
by
Pierre Aboulker,
Marko Radovanović,
Nicolas Trotignon,
Kristina
Vušković
Released
as a article
.
2013
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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1309.1841v1
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