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2008 | 28 | 3 | 477-486
Tytuł artykułu

The signed matchings in graphs

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let G be a graph with vertex set V(G) and edge set E(G). A signed matching is a function x: E(G) → {-1,1} satisfying $∑_{e ∈ E_G(v)} x(e) ≤ 1$ for every v ∈ V(G), where $E_G(v) = {uv ∈ E(G)| u ∈ V(G)}$. The maximum of the values of $∑_{e ∈ E(G)} x(e)$, taken over all signed matchings x, is called the signed matching number and is denoted by β'₁(G). In this paper, we study the complexity of the maximum signed matching problem. We show that a maximum signed matching can be found in strongly polynomial-time. We present sharp upper and lower bounds on β'₁(G) for general graphs. We investigate the sum of maximum size of signed matchings and minimum size of signed 1-edge covers. We disprove the existence of an analogue of Gallai's theorem. Exact values of β'₁(G) of several classes of graphs are found.
Wydawca
Rocznik
Tom
28
Numer
3
Strony
477-486
Opis fizyczny
Daty
wydano
2008
otrzymano
2007-12-18
poprawiono
2008-05-08
zaakceptowano
2008-07-28
Twórcy
  • Department of Mathematics, Ryerson University, Toronto, ON, Canada, M5B 2K3
Bibliografia
  • [1] R.P. Anstee, A polynomial algorithm for b-matchings: an alternative approach, Inform. Process. Lett. 24 (1987) 153-157, doi: 10.1016/0020-0190(87)90178-5.
  • [2] A. Bonato, K. Cameron and C. Wang, Signed b-edge covers of graphs, submitted.
  • [3] G. Chartrand and L. Lesniak, Graphs & Digraphs, third edition (Chapman and Hall, Boca Raton, 2000).
  • [4] W. Chena and E. Song, Lower bounds on several versions of signed domination number, Discrete Math. 308 (2008) 1837-1846, doi: 10.1016/j.disc.2006.09.050.
  • [5] S. Goodman, S. Hedetniemi and R.E. Tarjan, b-matchings in trees, SIAM J. Comput. 5 (1976) 104-108, doi: 10.1137/0205009.
  • [6] D. Hausmann, Adjacent vertices on the b-matching polyhedron, Discrete Math. 33 (1981) 37-51, doi: 10.1016/0012-365X(81)90256-9.
  • [7] H. Karami, S.M. Sheikholeslami and A. Khodkar, Some notes on signed edge domination in graphs, Graphs and Combin. 24 (2008) 29-35, doi: 10.1007/s00373-007-0762-8.
  • [8] W.R. Pulleyblank, Total dual integrality and b-matchings, Oper. Res. Lett. 1 (1981/82) 28-33, doi: 10.1016/0167-6377(81)90021-3.
  • [9] A. Schrijver, Combinatorial Optimization: polyhedra and efficiency (Berlin, Springer, 2004).
  • [10] C. Wang, The signed star domination numbers of the Cartesian product graphs, Discrete Appl. Math. 155 (2007) 1497-1505, doi: 10.1016/j.dam.2007.04.008.
  • [11] B. Xu, On signed edge domination numbers of graphs, Discrete Math. 239 (2001) 179-189, doi: 10.1016/S0012-365X(01)00044-9.
  • [12] B. Xu, Note On edge domination numbers of graphs, Discrete Math. 294 (2005) 311-316, doi: 10.1016/j.disc.2004.11.008.
  • [13] B. Xu, Two classes of edge domination in graphs, Discrete Appl. Math. 154 (2006) 1541-1546, doi: 10.1016/j.dam.2005.12.007.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1421
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