On Edge-Decomposition of Cubic Graphs into Copies of the Double-Star with Four Edges
A tree containing exactly two non-pendant vertices is called a double-star. Let k1 and k2 be two positive integers. The double-star with degree sequence (k1+1, k2+1, 1, ..., 1) is denoted by Sk1, k2. It is known that a cubic graph has an S1,1-decomposition if and only if it contains...
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| Format: | Article |
| Language: | English |
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University of Kashan
2018-06-01
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| Series: | Mathematics Interdisciplinary Research |
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| Online Access: | https://mir.kashanu.ac.ir/article_63511_00671cbdab52608c7230f8055860c91a.pdf |
| Summary: | A tree containing exactly two non-pendant vertices is called a double-star. Let k1 and k2 be two positive integers. The double-star with degree sequence (k1+1, k2+1, 1, ..., 1) is denoted by Sk1, k2. It is known that a cubic graph has an S1,1-decomposition if and only if it contains a perfect matching. In this paper, we study the S1,2-decomposition of cubic graphs. We present some necessary and some sufficient conditions for the existence of an S1,2-decomposition in cubic graphs. |
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| ISSN: | 2476-4965 |