Detecting an induced net subdivision

Authors:
Maria Chudnovsky;Paul Seymour;Nicolas Trotignon
Affiliations:
Columbia University, New York, NY 10027, United States;Princeton University, Princeton, NJ 08544, United States;CNRS, LIP - ENS Lyon, 15 parvis René Descartes, BP 7000, 69342 Lyon Cedex 07, France
Venue:
Journal of Combinatorial Theory Series B
Year:
2013

Citing 3
Cited 0

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Detecting induced subgraphs

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The three-in-a-tree problem

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Abstract

A net is a graph consisting of a triangle C and three more vertices, each of degree one and with its neighbour in C, and all adjacent to different vertices of C. We give a polynomial-time algorithm to test whether an input graph has an induced subgraph which is a subdivision of a net. Unlike many similar questions, this does not seem to be solvable by an application of the ''three-in-a-tree'' subroutine.