## Abstract For a graph __G__, we denote by __d__~__G__~(__x__) and ΞΊ(__G__) the degree of a vertex __x__ in __G__ and the connectivity of __G__, respectively. In this article, we show that if __G__ is a 3βconnected graph of order __n__ such that __d__~__G__~(__x__) + __d__~__G__~(__y__) + __d__~__
A degree sum condition for graphs to be covered by two cycles
β Scribed by Shuya Chiba; Masao Tsugaki
- Book ID
- 108114219
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 457 KB
- Volume
- 310
- Category
- Article
- ISSN
- 0012-365X
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π SIMILAR VOLUMES
For a graph G, let Ο 3 (G) = min{deg G x + deg G y + deg G z: {x, y, z} is an independent set in G}. Enomoto et al. [Enowoto et al., J Graph Theory 20 (1995), 419-422] have proved that the vertex set of a 2-connected graph G of order n with Ο 3 (G) β₯ n is covered by two cycles, edges or vertices. Ex
## Abstract Given a fixed multigraph __H__ with __V__(__H__)β=β{__h__~1~,β¦, __h__~m~}, we say that a graph __G__ is __H__βlinked if for every choice of __m__ vertices __v__~1~, β¦, ~v~~m~ in __G__, there exists a subdivision of __H__ in __G__ such that for every __i__, __v__~i~ is the branch vertex