We show that if G is a 3-connected graph of order at least seven, then every longest path between distinct vertices in G contains at least two contractible edges. An immediate corollary is that longest cycles in such graphs contain at least three contractible edges. We consider only finite undirect
Removable Edges in Longest Cycles of 4-Connected Graphs
β Scribed by Jichang Wu; Xueliang Li
- Publisher
- Springer Japan
- Year
- 2004
- Tongue
- English
- Weight
- 282 KB
- Volume
- 20
- Category
- Article
- ISSN
- 0911-0119
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Let G be a connected graph, where k 2. S. Smith conjectured that every two longest cycles of G have at least k vertices in common. In this note, we show that every two longest cycles meet in at least ck 3Γ5 vertices, where cr0.2615. ## 1998 Academic Press In this note, we provide a lower bound on
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