We prove that the vertex set of a simple graph with minimum degree at least s + t -1 and girth at least 5 can be decomposed into two parts, which induce subgraphs with minimum degree at least s and t, respectively, where s, t are positive integers ≥ 2.
✦ LIBER ✦
Sparse graphs of girth at least five are packable
✍ Scribed by Agnieszka Görlich; Andrzej Żak
- Book ID
- 119227547
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 245 KB
- Volume
- 312
- Category
- Article
- ISSN
- 0012-365X
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## Abstract Jeager et al. introduced a concept of group connectivity as a generalization of nowhere zero flows and its dual concept group coloring, and conjectured that every 5‐edge connected graph is Z~3~‐connected. For planar graphs, this is equivalent to that every planar graph with girth at lea