On claw-decomposition of a complete multipartite graph

Ushio, Kazuhiko; Tazawa, Shinsei; Yamamoto, Sumiyasu

doi:10.32917/hmj/1206135570

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Introduction4

Balanced S K -Decomposition and Center Balanced S K -Decompo1

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2023

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Cited by 24 publications

(7 citation statements)

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“…We check that the orientation satisfies (7)- (10). From the construction of the orientation, it is easy to see that for all y j ∈ N, and all x i , x i ∈ M, we have…”

Section: Balanced S K -Decomposition and Center Balanced S K -Decompomentioning

confidence: 98%

Balanced star decompositions of regular multigraphs and λ-fold complete bipartite graphs

Lee

Lin

2005

Discrete Mathematics

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Let S k denote the star with k edges. A balanced S k -decomposition of a multigraph G is a family D of subgraphs of G whose edge sets form a partition of the edge set of G such that each member of D is isomorphic to S k , and every vertex of G belongs to the same number of members in D. In this paper, we obtain the following results:(1) A necessary and sufficient condition for an r-regular multigraph to have a balanced S kdecomposition.(2) A necessary and sufficient condition for the -fold complete bipartite graph K m,n to have a balanced S k -decomposition.

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“…We check that the orientation satisfies (7)- (10). From the construction of the orientation, it is easy to see that for all y j ∈ N, and all x i , x i ∈ M, we have…”

Section: Balanced S K -Decomposition and Center Balanced S K -Decompomentioning

confidence: 98%

Balanced star decompositions of regular multigraphs and λ-fold complete bipartite graphs

Lee

Lin

2005

Discrete Mathematics

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“…Study of H-decomposition of graphs is not new. Many authors around the world are working in the field of cycle decomposition [4,8,9,21,22], path decomposition [24,25], star decompositon [19,23,26,27] and Hamilton cycle decomposition [2,3,15,16] problems in graphs. Here we consider the sunlet decomposition of product graphs.…”

Section: Introductionmentioning

confidence: 99%

Decomposition of product graphs into sunlet graphs of order eight

Sowndhariya

Muthusamy

2021

Journal of Algebra Combinatorics Discrete Structures and Applications

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“…Cycle decomposition of graphs and star decomposition of graphs are popular topic of research in graph theory; see [3,[12][13][14]. The study of ðK, HÞ -multidecomposition has been introduced by Atif Abueida and M. Daven [1].…”

Section: Introductionmentioning

confidence: 99%