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A note on signed k-matching in graphs

Akbari, S ; Sharif University of Technology | 2016

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  1. Type of Document: Article
  2. Publisher: University of Queensland , 2016
  3. Abstract:
  4. Let G be a graph of order n. For every v ∈ V (G), let EG(v) denote the set of all edges incident with v. A signed k-matching of G is a function f : E(G) −→ {−1, 1}, satisfying f(EG(v)) ≤ 1 for at least k vertices, where f(S) = ∑e∈S f(e), for each S ⊆ E(G). The maximum of the values of f(E(G)), taken over all signed k-matchings f of G, is called the signed k-matching number and is denoted by βk S (G). In this paper, we prove that for every graph G of order n and for any positive integer k ≤ n, βk S (G) ≥ n −k −ω(G), where w(G) is the number of components of G. This settles a conjecture proposed by Wang. Also, we present a formula for the computation of βn S(G)
  5. Keywords:
  7. Source: Australasian Journal of Combinatorics ; Volume 64, Issue 2 , 2016 , Pages 341-346 ; 10344942 (ISSN)
  8. URL: https://arxiv.org/abs/1411.0132