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Maximal Chordal Subgraphs
- Publication Year :
- 2022
-
Abstract
- A chordal graph is a graph with no induced cycles of length at least $4$. Let $f(n,m)$ be the maximal integer such that every graph with $n$ vertices and $m$ edges has a chordal subgraph with at least $f(n,m)$ edges. In 1985 Erd\H{o}s and Laskar posed the problem of estimating $f(n,m)$. In the late '80s, Erd\H{o}s, Gy\'arf\'as, Ordman and Zalcstein determined the value of $f(n,n^2/4+1)$ and made a conjecture on the value of $f(n,n^2/3+1)$. In this paper we prove this conjecture and answer the question of Erd\H{o}s and Laskar, determining $f(n,m)$ asymptotically for all $m$ and exactly for $m \leq n^2/3+1$.
- Subjects :
- Mathematics - Combinatorics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2205.08474
- Document Type :
- Working Paper