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.
@article{bwmeta1.element.doi-10_7151_dmgt_1933,
author = {Saieed Akbari and Shahab Haghi and Hamidreza Maimani and Abbas Seify},
title = {On Double-Star Decomposition of Graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {37},
year = {2017},
pages = {835-840},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1933}
}
Saieed Akbari; Shahab Haghi; Hamidreza Maimani; Abbas Seify. On Double-Star Decomposition of Graphs. Discussiones Mathematicae Graph Theory, Tome 37 (2017) pp. 835-840. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1933/