We show that every n-vertex cubic graph with girth at least g have domination number at most 0.299871n+O(n / g) < 3n / 10+O(n / g) This research was done when the Petr Ε koda was a student of
The Domination Number of Cubic Graphs with Girth at least Five
β Scribed by David C. Fisher; Kathryn Fraughnaugh; Suzanne M. Seager
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 356 KB
- Volume
- 11
- Category
- Article
- ISSN
- 1571-0653
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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 β₯ 2.
## 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 5βedge connected graph is Z~3~βconnected. For planar graphs, this is equivalent to that every planar graph with girth at lea
The closed neighborhood of a vertex subset S of a graph G = (V,E), denoted as N[Sj, is defined ss the union of S and the set of all the vertices adjacent to some vertex of S. A dominating set of a graph G = (V, E) is defined as a set S of vertices such that N[q = V. The domination number of a graph