The size of chordal, interval and threshold subgraphs

Abstract

Given a graphG withn vertices andm edges, how many edges must be in the largest chordal subgraph ofG? Form=n 2/4+1, the answer is 3n/2−1. Form=n 2/3, it is 2n−3. Form=n 2/3+1, it is at least 7n/3−6 and at most 8n/3−4. Similar questions are studied, with less complete results, for threshold graphs, interval graphs, and the stars on edges, triangles, andK 4's.

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This work was done while the authors were at Memphis State University, Memphis, Tennessee, USA.

Partially supported by National Science Foundation Grant DCR-8503922.

Partially supported by National Science Foundation Grant DCR-8602319 at Memphis State University.

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Erdös, P., Gyárfás, A., Ordman, E.T. et al. The size of chordal, interval and threshold subgraphs. Combinatorica 9, 245–253 (1989). https://doi.org/10.1007/BF02125893

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AMS subject classification (1980)

  • 05 C 35