Perfect edge domination: hard and solvable cases
Let G be an undirected graph. An edge of Gdominates itself and all edges adjacent to it. A subset E′ of edges of G is an edge dominating set of G, if every edge of the graph is dominated by some edge of E′. We say that E′ is a perfect edge dominating set of G, if every edge not in E′ is dominated by...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_02545330_v264_n1-2_p287_Lin |
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todo:paper_02545330_v264_n1-2_p287_Lin2023-10-03T15:11:35Z Perfect edge domination: hard and solvable cases Lin, M.C. Lozin, V. Moyano, V.A. Szwarcfiter, J.L. Claw-free graphs Complexity dichotomy Cubic graphs NP-completeness Perfect edge domination Let G be an undirected graph. An edge of Gdominates itself and all edges adjacent to it. A subset E′ of edges of G is an edge dominating set of G, if every edge of the graph is dominated by some edge of E′. We say that E′ is a perfect edge dominating set of G, if every edge not in E′ is dominated by exactly one edge of E′. The perfect edge dominating problem is to determine a least cardinality perfect edge dominating set of G. For this problem, we describe two NP-completeness proofs, for the classes of claw-free graphs of degree at most 3, and for bounded degree graphs, of maximum degree at most d≥ 3 and large girth. In contrast, we prove that the problem admits an O(n) time solution, for cubic claw-free graphs. In addition, we prove a complexity dichotomy theorem for the perfect edge domination problem, based on the results described in the paper. Finally, we describe a linear time algorithm for finding a minimum weight perfect edge dominating set of a P5-free graph. The algorithm is robust, in the sense that, given an arbitrary graph G, either it computes a minimum weight perfect edge dominating set of G, or it exhibits an induced subgraph of G, isomorphic to a P5. © 2017, Springer Science+Business Media, LLC. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_02545330_v264_n1-2_p287_Lin |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Claw-free graphs Complexity dichotomy Cubic graphs NP-completeness Perfect edge domination |
| spellingShingle |
Claw-free graphs Complexity dichotomy Cubic graphs NP-completeness Perfect edge domination Lin, M.C. Lozin, V. Moyano, V.A. Szwarcfiter, J.L. Perfect edge domination: hard and solvable cases |
| topic_facet |
Claw-free graphs Complexity dichotomy Cubic graphs NP-completeness Perfect edge domination |
| description |
Let G be an undirected graph. An edge of Gdominates itself and all edges adjacent to it. A subset E′ of edges of G is an edge dominating set of G, if every edge of the graph is dominated by some edge of E′. We say that E′ is a perfect edge dominating set of G, if every edge not in E′ is dominated by exactly one edge of E′. The perfect edge dominating problem is to determine a least cardinality perfect edge dominating set of G. For this problem, we describe two NP-completeness proofs, for the classes of claw-free graphs of degree at most 3, and for bounded degree graphs, of maximum degree at most d≥ 3 and large girth. In contrast, we prove that the problem admits an O(n) time solution, for cubic claw-free graphs. In addition, we prove a complexity dichotomy theorem for the perfect edge domination problem, based on the results described in the paper. Finally, we describe a linear time algorithm for finding a minimum weight perfect edge dominating set of a P5-free graph. The algorithm is robust, in the sense that, given an arbitrary graph G, either it computes a minimum weight perfect edge dominating set of G, or it exhibits an induced subgraph of G, isomorphic to a P5. © 2017, Springer Science+Business Media, LLC. |
| format |
JOUR |
| author |
Lin, M.C. Lozin, V. Moyano, V.A. Szwarcfiter, J.L. |
| author_facet |
Lin, M.C. Lozin, V. Moyano, V.A. Szwarcfiter, J.L. |
| author_sort |
Lin, M.C. |
| title |
Perfect edge domination: hard and solvable cases |
| title_short |
Perfect edge domination: hard and solvable cases |
| title_full |
Perfect edge domination: hard and solvable cases |
| title_fullStr |
Perfect edge domination: hard and solvable cases |
| title_full_unstemmed |
Perfect edge domination: hard and solvable cases |
| title_sort |
perfect edge domination: hard and solvable cases |
| url |
http://hdl.handle.net/20.500.12110/paper_02545330_v264_n1-2_p287_Lin |
| work_keys_str_mv |
AT linmc perfectedgedominationhardandsolvablecases AT lozinv perfectedgedominationhardandsolvablecases AT moyanova perfectedgedominationhardandsolvablecases AT szwarcfiterjl perfectedgedominationhardandsolvablecases |
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1807323766161670144 |