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On Decomposing Regular Graphs Into Isomorphic Double-Stars

100%

El-Zanati S. I., Ermete M., Hasty J., Plantholt M. J., Tipnis S.

Discussiones Mathematicae Graph Theory

2015

tom 35

nr 1

73-79

A double-star is a tree with exactly two vertices of degree greater than 1. If T is a double-star where the two vertices of degree greater than one have degrees k1+1 and k2+1, then T is denoted by Sk1,k2 . In this note, we show that every double-star with n edges decomposes every 2n-regular graph. We also show that the double-star Sk,k−1 decomposes every 2k-regular graph that contains a perfect matching.

On Double-Star Decomposition of Graphs

80%

Akbari S., Haghi S., Maimani H., Seify A.

Discussiones Mathematicae Graph Theory

2017

tom 37

nr 3

835-840

A tree containing exactly two non-pendant vertices is called a double-star. A double-star with degree sequence (k1 + 1, k2 + 1, 1, . . . , 1) is denoted by Sk1,k2. We study the edge-decomposition of graphs into double-stars. It was proved that every double-star of size k decomposes every 2k-regular graph. In this paper, we extend this result by showing that every graph in which every vertex has degree 2k + 1 or 2k + 2 and containing a 2-factor is decomposed into Sk1,k2 and Sk1−1,k2, for all positive integers k1 and k2 such that k1 + k2 = k.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

1 Akbari S.

1 El-Zanati S. I.

1 Ermete M.

1 Haghi S.

1 Hasty J.

1 Maimani H.

1 Plantholt M. J.

1 Seify A.

1 Tipnis S.

1 2017

1 2015

Wyniki wyszukiwania

On Decomposing Regular Graphs Into Isomorphic Double-Stars

On Double-Star Decomposition of Graphs