Some gregarious cycle decompositions of complete equipartite graphs.
Smith, Benjamin R. (2009)
The Electronic Journal of Combinatorics [electronic only]
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Smith, Benjamin R. (2009)
The Electronic Journal of Combinatorics [electronic only]
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Shanmugasundaram Jeevadoss, Appu Muthusamy (2015)
Discussiones Mathematicae Graph Theory
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We give necessary and sufficient conditions for the decomposition of complete bipartite multigraph Km,n(λ) into paths and cycles having k edges. In particular, we show that such decomposition exists in Km,n(λ), when λ ≡ 0 (mod 2), [...] and k(p + q) = 2mn for k ≡ 0 (mod 2) and also when λ ≥ 3, λm ≡ λn ≡ 0(mod 2), k(p + q) =λ_mn, m, n ≥ k, (resp., m, n ≥ 3k/2) for k ≡ 0(mod 4) (respectively, for k ≡ 2(mod 4)). In fact, the necessary conditions given above are also sufficient when λ =...
Lidia Badura (2014)
Discussiones Mathematicae Graph Theory
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Let G = G1 ∪ G2 be the sum of two simple graphs G1,G2 having a common edge or G = G1 ∪ e1 ∪ e2 ∪ G2 be the sum of two simple disjoint graphs G1,G2 connected by two edges e1 and e2 which form a cycle C4 inside G. We give a method of computing the determinant det A(G) of the adjacency matrix of G by reducing the calculation of the determinant to certain subgraphs of G1 and G2. To show the scope and effectiveness of our method we give some examples
Jordon, Heather (2011)
The Electronic Journal of Combinatorics [electronic only]
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Smith, Benjamin R., Cavenagh, Nicholas J. (2010)
The Electronic Journal of Combinatorics [electronic only]
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Dalibor Froncek, Michael Kubesa (2011)
Open Mathematics
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We solve the last missing case of a “two delegation negotiation” version of the Oberwolfach problem, which can be stated as follows. Suppose we have two negotiating delegations with n=mk members each and we have a seating arrangement such that every day the negotiators sit at m tables with k people of the same delegation at one side of each table. Every person can effectively communicate just with three nearest persons across the table. Our goal is to guarantee that over the course of...
Gould, Ronald, Łuczak, Tomasz, Schmitt, John (2006)
The Electronic Journal of Combinatorics [electronic only]
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Fleming, Thomas, Diesl, Alexander (2005)
Algebraic & Geometric Topology
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Lazebnik, Felix, Verstraëte, Jacques (2003)
The Electronic Journal of Combinatorics [electronic only]
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Fairouz Beggas, Mohammed Haddad, Hamamache Kheddouci (2015)
Discussiones Mathematicae Graph Theory
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Let k be a positive integer, Sk and Ck denote, respectively, a star and a cycle of k edges. λKn is the usual notation for the complete multigraph on n vertices and in which every edge is taken λ times. In this paper, we investigate necessary and sufficient conditions for the existence of the decomposition of λKn into edges disjoint of stars Sk’s and cycles Ck’s.