Edge-connectivity in -path graphs
✍ Scribed by C. Balbuena; P. García-Vázquez
- Book ID
- 108113457
- Publisher
- Elsevier Science
- Year
- 2004
- Tongue
- English
- Weight
- 184 KB
- Volume
- 286
- Category
- Article
- ISSN
- 0012-365X
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## Abstract We consider finite undirected loopless graphs __G__ in which multiple edges are possible. For integers k,l ≥ 0 let g(k, l) be the minimal __n__ ≥ 0 with the following property: If __G__ is an __n__‐edge‐connected graph, __s__~1~, ⃛,__s__~k~, __t__~1~, ⃛,__t__~k~ are vertices of __G__, a
Let G = (V, €1 be a finite, simple p-partite graph with minimum degree 6 and edge-connectivity A. It is proved that if IVI d (2pS)/(p -1) -2 or in special cases that if IVI I ( 2 p 6 ) / ( p -1) -1, then A = S . It is further shown that this result is best possible.