Graphs that do not contain a cycle with a node that has at least two neighbors on it
Aboulker, P, Radovanović, M, Trotignon, N et al. (1 more author)
(2012)
Graphs that do not contain a cycle with a node that has at least two neighbors on it.
SIAM Journal on Discrete Mathematics, 26 (4).
1510 - 1531.
ISSN 0895-4801
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 and polynomial time algorithms for vertex-coloring and edge-coloring.
Metadata
Item Type:
Article
Authors/Creators:
Aboulker, P
Radovanović, M
Trotignon, N
Vušković, K
Copyright, Publisher and Additional Information:
(c) 2012, Society for Industrial and Applied Mathematics. Reproduced in accordance with the publisher's self-archiving policy.
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