Edge-Decomposition of Graphs into Copies of a Tree with Four Edges
نویسندگان
چکیده
منابع مشابه
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 $k_1$ and $k_2$ be two positive integers. The double-star with degree sequence $(k_1+1, k_2+1, 1, ldots, 1)$ is denoted by $S_{k_1, k_2}$. It is known that a cubic graph has an $S_{1,1}$-decomposition if and only if it contains a perfect matching. In this paper, we study the $S_{1,2}$-decomposit...
متن کاملEdge-decomposition of Graphs into Copies of a Tree with Four Edges
We study edge-decompositions of highly connected graphs into copies of a given tree. In particular we attack the following conjecture by Barát and Thomassen: for each tree T , there exists a natural number kT such that if G is a kT -edge-connected graph, and |E(T )| divides |E(G)|, then E(G) has a decomposition into copies of T . As one of our main results it is sufficient to prove the conjectu...
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The Tree Decomposition Conjecture by Barát and Thomassen states that for every tree T there exists a natural number k(T ) such that the following holds: If G is a k(T )-edge-connected simple graph with size divisible by the size of T , then G can be edge-decomposed into subgraphs isomorphic to T . So far this conjecture has only been verified for paths, stars, and a family of bistars. We prove ...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2014
ISSN: 1077-8926
DOI: 10.37236/2110