Let G be a connected claw-free graph on n vertices. Let Ο 3 (G) be the minimum degree sum among triples of independent vertices in G. It is proved that if Ο 3 (G) β₯ n-3 then G is traceable or else G is one of graphs G n each of which comprises three disjoint nontrivial complete graphs joined togethe
Traceability in Small Claw-Free Graphs
β Scribed by John M. Harris; Michael J. Mossinghoff
- Book ID
- 108497953
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 277 KB
- Volume
- 11
- Category
- Article
- ISSN
- 1571-0653
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π SIMILAR VOLUMES
A graph is said to be claw-free if it does not contain an induced subgraph isomorphic to KI,3. Let k be a positive integer. Our main result is as follows: If G is a claw-free graph of order at least 3k and d(x) + d(y)>~3k + 1 for every pair of non-adjacent vertices x and y of G, then G contains k v
A graph G is quasi claw-free if it satisfies the property: This property is satisfied if in particular u does not center a claw (induced K1.3). Many known results on claw-free graphs, dealing with matching and hamiltonicity are extended to the larger class of quasi-claw-free graphs.
## Abstract We say that __G__ is almost clawβfree if the vertices that are centers of induced claws (__K__~1,3~) in __G__ are independent and their neighborhoods are 2βdominated. Clearly, every clawβfree graph is almost clawβfree. It is shown that (i) every even connected almost clawβfree graph has