In this paper we prove the following conjecture of Woodall: if bind (G)≥3/2, thenG contains a triangle. Moreover we also prove that if bind (G)≥3/2, then each vertex is contained in a 4-cycle, each edge is contained in a 5-cycle whenV(G)≥11, and there exists a 6-cycle inG.
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Ronghua, S. The binding number of a graph and its triangle. Acta Mathematicae Applicatae Sinica 2, 79–86 (1985). https://doi.org/10.1007/BF01666521
- Math Application
- Binding Number