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On the star arboricity of hypercubes

Karisani, N ; Sharif University of Technology

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  1. Type of Document: Article
  2. Abstract:
  3. A hypercube Qn is a graph in which the vertices are all binary vectors of length n, and two vertices are adjacent if and only if their components differ in exactly one place. A galaxy or a star forest is a union of vertex disjoint stars. The star arboricity of a graph G, sa(G), is the minimum number of galaxies which partition the edge set of G. In this paper among other results, we determine the exact values of sa(Qn) for n ∈ {2k - 3, 2k + 1, 2k + 2, 2i + 2j - 4}, i ≥ j ≥ 2. We also improve the last known upper bound of sa(Qn) and show the relation between sa(G) and square coloring
  4. Keywords:
  6. Source: Australasian Journal of Combinatorics ; Vol. 59, Issue. 2 , 2014 , pp. 282-292 ; ISSN: 1034-4942
  7. URL: http://www.sciencedirect.com/science/article/pii/0895717788904839