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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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Published in: | Journal of graph theory 2019-02, Vol.90 (2), p.137-149 |
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description | 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. |
doi_str_mv | 10.1002/jgt.22372 |
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subjects | Andrásfai graphs Apexes Erdõs (1/2,1/50)–conjecture Graph theory Graphs sparse halves triangle‐free graphs |
title | On the local density problem for graphs of given odd‐girth |
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