A polynomial time algorithm for the triangle packing problem on interval graphs

The triangle packing problem (TPP) is to find the maximum number of pairwise vertex disjoint triangles in a given graph. The TPP is NP-complete in a general graph and even so when a given graph is restricted to a chordal graph. On the other hand, the TPP can be solved in polynomial time for unit int...

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Bibliographic Details
Published in:Discrete Applied Mathematics Vol. 343; pp. 180 - 183
Main Author: Myung, Young-Soo
Format: Journal Article
Language:English
Published: Elsevier B.V 30.01.2024
Subjects:
Interval graph
Packing triangles
Polynomial time algorithm
Interval graph
Packing triangles
Polynomial time algorithm
ISSN:0166-218X
Online Access:Get full text
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Summary:The triangle packing problem (TPP) is to find the maximum number of pairwise vertex disjoint triangles in a given graph. The TPP is NP-complete in a general graph and even so when a given graph is restricted to a chordal graph. On the other hand, the TPP can be solved in polynomial time for unit interval graphs. For this reason, it is a well-known open problem to prove whether there exists a polynomial time algorithm solving the TPP on interval graphs. In this paper, we give an answer to the problem.
ISSN:0166-218X
DOI:10.1016/j.dam.2023.10.022