Wszystkie pola: connectivity - Katalog OPAC zbiorów

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Tytuł:: Cospectral Pairs of Regular Graphs with Different Connectivity
Autorzy:: Haemers, Willem H.
Powiązania:: https://bibliotekanauki.pl/articles/31552242.pdf
Data publikacji:: 2020-05-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: graph spectrum
vertex-connectivity
edge-connectivity
spectral characterization
Opis:: For vertex- and edge-connectivity we construct infinitely many pairs of regular graphs with the same spectrum, but with different connectivity.
Źródło:: Discussiones Mathematicae Graph Theory; 2020, 40, 2; 577-584
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: More on even [a,b]-factors in graphs
Autorzy:: Khodkar, Abdollah
Xu, Rui
Powiązania:: https://bibliotekanauki.pl/articles/743747.pdf
Data publikacji:: 2007
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: [a,b]-factor
spanning graph
edge-connectivity
Opis:: In this note we give a characterization of the complete bipartite graphs which have an even (odd) [a,b]-factor. For general graphs we prove that an a-edge connected graph G with n vertices and with δ(G) ≥ max{a+1,an/(a+b) + a - 2} has an even [a,b]-factor, where a and b are even and 2 ≤ a ≤ b. With regard to the edge-connectivity this result is slightly better than one of the similar results obtained by Kouider and Vestergaard in 2004 and unlike their results, this result has no restriction on the order of graphs.
Źródło:: Discussiones Mathematicae Graph Theory; 2007, 27, 1; 193-204
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: Sufficient Conditions for Maximally Edge-Connected and Super-Edge-Connected Graphs Depending on The Clique Number
Autorzy:: Volkmann, Lutz
Powiązania:: https://bibliotekanauki.pl/articles/31343389.pdf
Data publikacji:: 2019-05-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: edge-connectivity
clique number
maximally edge-connected graphs
super-edge-connected graphs
Opis:: Let G be a connected graph with minimum degree δ and edge-connectivity λ. A graph is maximally edge-connected if λ = δ, and it is super-edgeconnected if every minimum edge-cut is trivial; that is, if every minimum edge-cut consists of edges incident with a vertex of minimum degree. The clique number ω(G) of a graph G is the maximum cardinality of a complete subgraph of G. In this paper, we show that a connected graph G with clique number ω(G) ≤ r is maximally edge-connected or super-edge-connected if the number of edges is large enough. These are generalizations of corresponding results for triangle-free graphs by Volkmann and Hong in 2017.
Źródło:: Discussiones Mathematicae Graph Theory; 2019, 39, 2; 567-573
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 4.

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

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