Complete bipartite decompositions of crowns, with applications to complete directed graphs

Lin, Chiang; Lin, Jenq-Jong; Shyu, Tay-Woei

doi:10.1007/3-540-61576-8_74

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2024

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“…We will use the following theorem on the least common multiple of two bipartite graphs, by O. Favaron and C. M. Mynhardt. Before entering the path decomposition, star decomposition, and crown decomposition, we consider the decomposition of bipartite graphs in [9]. Suppose that G is a bipartite graph with bipartition (X, Y ), where X = {x 1 , x 2 , .…”

Section: Preliminariesmentioning

confidence: 99%

Common Multiples of Paths and Stars with Crowns

Chandran C.,

2024

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A graph $G$ is a common multiple of two graphs $H_1$ and $H_2$ if there exists a decomposition of $G$ into edge-disjoint copies of $H_1$ and also a decomposition of $G$ into edge-disjoint copies of $H_2$. If $ G $ is a common multiple of $H_1$ and $H_2$, and $ G $ has $ q $ edges, then we call $ G $ a $ (q, H_1, H_2) $ graph. Our paper deals with the following question: Given two graphs $ H_1 $ and $ H_2$, for which values of $ q $ does there exist a $ (q, H_1, H_2) $ graph? when $H_1$ is either a path or a star with $3$ or $4$ edges and $H_2$ is a crown.

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Section: Preliminariesmentioning

confidence: 99%

Common Multiples of Paths and Stars with Crowns

Chandran C.,

2024

Proyecciones (Antofagasta)

View full text Add to dashboard Cite

show abstract

Complete bipartite decompositions of crowns, with applications to complete directed graphs

Cited by 1 publication

References 9 publications

Common Multiples of Paths and Stars with Crowns

Common Multiples of Paths and Stars with Crowns

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