A characterization of 2-tree probe interval graphs

Brown, David E.; Flesch, Breeann; Richard, Jean‐Marc

doi:10.7151/dmgt.1754

Cited by 1 publication

(3 citation statements)

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“…We have introduced, implemented and tested an efficient non-partitioned recognition algorithm for 2-trees, an extension of trees, that are probe interval graphs. Our algorithm is based on a structure called a sparse spiny interval 2-lobster introduced in [11]. The complexity of our approach is O(n 2 ) or O(m).…”

Section: Discussionmentioning

confidence: 99%

“…Pržulj and Corneil investigated a forbidden induced subgraph characterization for 2-tree probe interval graphs in [10], finding that there are at least 62 forbidden subgraphs. This large obstruction set was added to in [11], where Brown, et al found one more infinite family of forbidden subgraphs. In that paper, there was a complete characterization of 2-tree probe interval graphs based on a structure called a sparse spiny interval 2-lobster (ssi2-lobster).…”

Section: Foundationsmentioning

confidence: 99%

“…Theorem 2.1. [11] Let G be a 2−tree. Then G is a probe interval graph if and only if it is an ssi2-lobster.…”

Section: Foundationsmentioning

confidence: 99%

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Recognition Algorithm for Probe Interval 2-Trees

Flesch

Nabity

2016

BJMCS

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Recognition of probe interval graphs has been studied extensively. Recognition algorithms of probe interval graphs can be broken down into two types of problems: partitioned and non-partitioned. A partitioned recognition algorithm includes the probe and nonprobe partition of the vertices as part of the input, where a non-partitioned algorithm does not include the partition. Partitioned probe interval graphs can be recognized in linear-time in the edges, whereas non-partitioned probe interval graphs can be recognized in polynomial-time. Here we present a non-partitioned recognition algorithm for 2-trees, an extension of trees, that are probe interval graphs. We show that this algorithm runs in O(m) time, where m is the number of edges of a 2-tree. Currently there is no algorithm that performs as well for this problem.

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Section: Discussionmentioning

confidence: 99%

Section: Foundationsmentioning

confidence: 99%