- Tytuł:
- Counterexample to a conjecture on the structure of bipartite partitionable graphs
- Autorzy:
-
Gibson, Richard
Mynhardt, Christina - Powiązania:
- https://bibliotekanauki.pl/articles/743437.pdf
- Data publikacji:
- 2007
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
domination
prism fixer
symmetric dominating set
bipartite graph - Opis:
-
A graph G is called a prism fixer if γ(G×K₂) = γ(G), where γ(G) denotes the domination number of G. A symmetric γ-set of G is a minimum dominating set D which admits a partition D = D₁∪ D₂ such that $V(G)-N[D_i] = D_j$, i,j = 1,2, i ≠ j. It is known that G is a prism fixer if and only if G has a symmetric γ-set.
Hartnell and Rall [On dominating the Cartesian product of a graph and K₂, Discuss. Math. Graph Theory 24 (2004), 389-402] conjectured that if G is a connected, bipartite graph such that V(G) can be partitioned into symmetric γ-sets, then G ≅ C₄ or G can be obtained from $K_{2t,2t}$ by removing the edges of t vertex-disjoint 4-cycles. We construct a counterexample to this conjecture and prove an alternative result on the structure of such bipartite graphs. - Źródło:
-
Discussiones Mathematicae Graph Theory; 2007, 27, 3; 527-540
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł