Embedding edge‐colorings into 2‐edge‐connected k‐factorizations of kkn+1

Rodger, C. A.; Wantland, Evan B.

doi:10.1002/jgt.3190190205

Cited by 28 publications

(37 citation statements)

References 17 publications

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“…We aim to show that the converse is also true. We will show this by proving that any outline 2-factorization G of K p m has a disentanglement G H that is also a 2-factorization of K p m , a result that was ®rst proved by Wantland and Rodger [10]. However, here we will do even more.…”

Section: Amalgamations and Outline 2-factorizationsmentioning

confidence: 91%

Nondisconnecting disentanglements of amalgamated 2‐factorizations of complete multipartite graphs

Leach¹,

Rodger²

2001

J of Combinatorial Designs

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In this paper necessary and suf®cient conditions are found for an edge-colored graph H to be the homomorphic image of a 2-factorization of a complete multipartite graph G in which each 2-factor of G has the same number of components as its corresponding color class in H. This result is used to completely solve the problem of ®nding hamilton decompositions of K aYb À EU for any 2-factor U of K aYb . #

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Section: Amalgamations and Outline 2-factorizationsmentioning

confidence: 91%

Nondisconnecting disentanglements of amalgamated 2‐factorizations of complete multipartite graphs

Leach¹,

Rodger²

2001

J of Combinatorial Designs

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“…At the end of the next section we shall give a proof using amalgamations. Many combinatorial problems have been solved using amalgamations; see, for example, [1][2][3][4]6,7,11]. Let us sketch how we will use the technique on (t, K, L)-factorizations of K n .…”

Section: Introductionmentioning

confidence: 99%

Amalgamations of factorizations of complete graphs

Johnson

2007

Journal of Combinatorial Theory, Series B

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Let t be a positive integer, and let K = (k 1 , . . . , k t ) and L = (l 1 , . . . , l t ) be collections of nonnegative integers. A (t, K, L)-factorization of a graph is a decomposition of the graph into factors F 1 , . . . , F t such that F i is k i -regular and l i -edge-connected. In this paper, we apply the technique of amalgamations of graphs to study (t, K, L)-factorizations of complete graphs. In particular, we describe precisely when it is possible to embed a factorization of K m in a (t, K, L)-factorization of K n .

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“…The method of proof used to obtain this result is the method of amalgamations, which is of interest in its own right. It has also been successfully used in similar circumstances (for example, see [5,6,13]). …”

Section: Introductionmentioning

confidence: 95%