On the local density problem for graphs of given odd‐girth

Erdős conjectured that every n‐vertex triangle‐free graph contains a subset of ⌊n/2⌋ vertices that spans at most n2/50 edges. Extending a recent result of Norin and Yepremyan, we confirm this conjecture for graphs homomorphic to so‐called Andrásfai graphs. As a consequence, Erdős' conjecture ho...

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Bibliographic Details
Published in:Journal of graph theory 2019-02, Vol.90 (2), p.137-149
Main Authors: Bedenknecht, Wiebke, Mota, Guilherme Oliveira, Reiher, Christian, Schacht, Mathias
Format: Article
Language:English
Subjects:
Andrásfai graphs
Apexes
Erdõs (1/2,1/50)–conjecture
Graph theory
Graphs
sparse halves
triangle‐free graphs
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Summary:Erdős conjectured that every n‐vertex triangle‐free graph contains a subset of ⌊n/2⌋ vertices that spans at most n2/50 edges. Extending a recent result of Norin and Yepremyan, we confirm this conjecture for graphs homomorphic to so‐called Andrásfai graphs. As a consequence, Erdős' conjecture holds for every triangle‐free graph G with minimum degree δ(G)>10n/29 and if χ(G)≤3 the degree condition can be relaxed to δ(G)>n/3. In fact, we obtain a more general result for graphs of higher odd‐girth.
ISSN:0364-9024
1097-0118
DOI:10.1002/jgt.22372