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Wyświetlanie 1-7 z 7
Tytuł:
The NP-completeness of automorphic colorings
Autorzy:
Mazzuoccolo, Giuseppe
Powiązania:
https://bibliotekanauki.pl/articles/744108.pdf
Data publikacji:
2010
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
NP-complete problems
chromatic parameters
graph coloring
computational complexity
Opis:
Given a graph G, an automorphic edge(vertex)-coloring of G is a proper edge(vertex)-coloring such that each automorphism of the graph preserves the coloring. The automorphic chromatic index (number) is the least integer k for which G admits an automorphic edge(vertex)-coloring with k colors. We show that it is NP-complete to determine the automorphic chromatic index and the automorphic chromatic number of an arbitrary graph.
Źródło:
Discussiones Mathematicae Graph Theory; 2010, 30, 4; 705-710
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Semitotal Domination Problem in Block Graphs
Autorzy:
Henning, Michael A.
Pal, Saikat
Pradhan, D.
Powiązania:
https://bibliotekanauki.pl/articles/32361741.pdf
Data publikacji:
2022-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
domination
semitotal domination
block graphs
undirected path graphs
NP-complete
Opis:
A set D of vertices in a graph G is a dominating set of G if every vertex outside D is adjacent in G to some vertex in D. A set D of vertices in G is a semitotal dominating set of G if D is a dominating set of G and every vertex in D is within distance 2 from another vertex of D. Given a graph G and a positive integer k, the semitotal domination problem is to decide whether G has a semitotal dominating set of cardinality at most k. The semitotal domination problem is known to be NP-complete for chordal graphs and bipartite graphs as shown in [M.A. Henning and A. Pandey, Algorithmic aspects of semitotal domination in graphs, Theoret. Comput. Sci. 766 (2019) 46–57]. In this paper, we present a linear time algorithm to compute a minimum semitotal dominating set in block graphs. On the other hand, we show that the semitotal domination problem remains NP-complete for undirected path graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2022, 42, 1; 231-248
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Split Euler Tours In 4-Regular Planar Graphs
Autorzy:
Couch, PJ
Daniel, B.D.
Guidry, R.
Paul Wright, W.
Powiązania:
https://bibliotekanauki.pl/articles/31341188.pdf
Data publikacji:
2016-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
4-regular
3-connected
planar
split Euler tour
NP-complete
Opis:
The construction of a homing tour is known to be NP-complete. On the other hand, the Euler formula puts su cient restrictions on plane graphs that one should be able to assert the existence of such tours in some cases; in particular we focus on split Euler tours (SETs) in 3-connected, 4-regular, planar graphs (tfps). An Euler tour S in a graph G is a SET if there is a vertex v (called a half vertex of S) such that the longest portion of the tour between successive visits to v is exactly half the number of edges of G. Among other results, we establish that every tfp G having a SET S in which every vertex of G is a half vertex of S can be transformed to another tfp G′ having a SET S′ in which every vertex of G′ is a half vertex of S′ and G′ has at most one point having a face configuration of a particular class. The various results rely heavily on the structure of such graphs as determined by the Euler formula and on the construction of tfps from the octahedron. We also construct a 2-connected 4-regular planar graph that does not have a SET.
Źródło:
Discussiones Mathematicae Graph Theory; 2016, 36, 1; 23-30
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Complexity of Secure Domination Problem in Graphs
Autorzy:
Wang, Haichao
Zhao, Yancai
Deng, Yunping
Powiązania:
https://bibliotekanauki.pl/articles/31342335.pdf
Data publikacji:
2018-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
secure domination
star convex bipartite graph
doubly chordal graph
NP-complete
APX-complete
Opis:
A dominating set of a graph G is a subset D ⊆ V (G) such that every vertex not in D is adjacent to at least one vertex in D. A dominating set S of G is called a secure dominating set if each vertex u ∈ V (G) \ S has one neighbor v in S such that (S \ {v}) ∪ {u} is a dominating set of G. The secure domination problem is to determine a minimum secure dominating set of G. In this paper, we first show that the decision version of the secure domination problem is NP-complete for star convex bipartite graphs and doubly chordal graphs. We also prove that the secure domination problem cannot be approximated within a factor of (1−ε) ln |V | for any ε > 0, unless NP⊆DTIME (|V |O(log log |V|)). Finally, we show that the secure domination problem is APX-complete for bounded degree graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2018, 38, 2; 385-396
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Spanning trees with many or few colors in edge-colored graphs
Autorzy:
Broersma, Hajo
Li, Xueliang
Powiązania:
https://bibliotekanauki.pl/articles/971955.pdf
Data publikacji:
1997
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
edge-coloring
spanning tree
matroid (intersection)
complexity
NP-complete
NP-hard
polynomial algorithm
(minimum) dominating set
Opis:
Given a graph G = (V,E) and a (not necessarily proper) edge-coloring of G, we consider the complexity of finding a spanning tree of G with as many different colors as possible, and of finding one with as few different colors as possible. We show that the first problem is equivalent to finding a common independent set of maximum cardinality in two matroids, implying that there is a polynomial algorithm. We use the minimum dominating set problem to show that the second problem is NP-hard.
Źródło:
Discussiones Mathematicae Graph Theory; 1997, 17, 2; 259-269
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Tabu Search approach in coherent co-synthesis of multiprocessors systems
Autorzy:
Drabowski, M.
Czajkowski, K.
Powiązania:
https://bibliotekanauki.pl/articles/92834.pdf
Data publikacji:
2006
Wydawca:
Uniwersytet Przyrodniczo-Humanistyczny w Siedlcach
Tematy:
synthesis of system
coherent
identification resources
task scheduling
NP-complete problem
heuristic algorithm
tabu search algorithm
Opis:
This paper presents the use of Tabu Search algorithm for solving the problems of coherent synthesis of multiprocessor computer systems. The paper includes a coherent solution of both optimization of partition resources and optimization of tasks scheduling. This publication shows results of computational experiments for different instances of system synthesis problems.
Źródło:
Studia Informatica : systems and information technology; 2006, 1(7); 31-45
1731-2264
Pojawia się w:
Studia Informatica : systems and information technology
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
More on the Rainbow Disconnection in Graphs
Autorzy:
Bai, Xuqing
Chang, Renying
Huang, Zhong
Li, Xueliang
Powiązania:
https://bibliotekanauki.pl/articles/32222544.pdf
Data publikacji:
2022-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
edge-coloring
edge-connectivity
rainbow disconnection coloring (number)
Erdős-Gallai type problem
Nordhaus-Gaddum type bounds
complexity
NP-hard (complete)
Opis:
Let G be a nontrivial edge-colored connected graph. An edge-cut R of G is called a rainbow-cut if no two of its edges are colored the same. An edge-colored graph G is rainbow disconnected if for every two vertices u and v of G, there exists a u-v-rainbow-cut separating them. For a connected graph G, the rainbow disconnection number of G, denoted by rd(G), is defined as the smallest number of colors that are needed in order to make G rainbow disconnected. In this paper, we first determine the maximum size of a connected graph G of order n with rd(G) = k for any given integers k and n with 1 ≤ k ≤ n − 1, which solves a conjecture posed only for n odd in [G. Chartrand, S. Devereaux, T.W. Haynes, S.T. Hedetniemi and P. Zhang, Rainbow disconnection in graphs, Discuss. Math. Graph Theory 38 (2018) 1007–1021]. From this result and a result in their paper, we obtain Erdős-Gallai type results for rd(G). Secondly, we discuss bounds on rd(G) for complete multipartite graphs, critical graphs with respect to the chromatic number, minimal graphs with respect to the chromatic index, and regular graphs, and we also give the values of rd(G) for several special graphs. Thirdly, we get Nordhaus-Gaddum type bounds for rd(G), and examples are given to show that the upper and lower bounds are sharp. Finally, we show that for a connected graph G, to compute rd(G) is NP-hard. In particular, we show that it is already NP-complete to decide if rd(G) = 3 for a connected cubic graph. Moreover, we show that for a given edge-colored (with an unbounded number of colors) connected graph G it is NP-complete to decide whether G is rainbow disconnected.
Źródło:
Discussiones Mathematicae Graph Theory; 2022, 42, 4; 1185-1204
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
    Wyświetlanie 1-7 z 7

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