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Some recent results on domination in graphs

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EN
Abstrakty
EN
In this paper, we survey some new results in four areas of domination in graphs, namely:
(1) the toughness and matching structure of graphs having domination number 3 and which are "critical" in the sense that if one adds any missing edge, the domination number falls to 2;
(2) the matching structure of graphs having domination number 3 and which are "critical" in the sense that if one deletes any vertex, the domination number falls to 2;
(3) upper bounds on the domination number of cubic graphs; and
(4) upper bounds on the domination number of graphs embedded in surfaces.
Słowa kluczowe
Twórcy
  • Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240, USA
Bibliografia
  • [1] N. Ananchuen and M.D. Plummer, Some results related to the toughness of 3-domination-critical graphs, Discrete Math. 272 (2003) 5-15, doi: 10.1016/S0012-365X(03)00179-1.
  • [2] N. Ananchuen and M.D. Plummer, Some results related to the toughness of 3-domination critical graphs, II, Utilitas Math. (2006), (to appear).
  • [3] N. Ananchuen and M.D. Plummer, Matching properties in domination critical graphs, Discrete Math. 277 (2004) 1-13, doi: 10.1016/S0012-365X(03)00243-7.
  • [4] N. Ananchuen and M.D. Plummer, 3-factor-criticality in domination critical graphs, (2005), (submitted).
  • [5] N. Ananchuen and M.D. Plummer, Matchings in 3-vertex-critical graphs: the even case, Networks 45 (2005) 210-213, doi: 10.1002/net.20065.
  • [6] N. Ananchuen and M.D. Plummer, Matchings in 3-vertex-critical graphs: the odd case, 2005, (submitted).
  • [7] N. Ananchuen and M.D. Plummer, On the connectivity and matchings in 3-vertex-critical claw-free graphs, Utilitas Math. (2006), (to appear).
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  • [23] A.V. Kostochka and B.Y. Stodolsky, On domination in connected cubic graphs, Communication: Discrete Math. 304 (2005) 45-50, doi: 10.1016/j.disc.2005.07.005.
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Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1338
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