Decompositions of a complete multidigraph into nonhamiltonian paths
✍ Scribed by Mariusz Meszka; Zdzisław Skupień
- Publisher
- John Wiley and Sons
- Year
- 2005
- Tongue
- English
- Weight
- 116 KB
- Volume
- 51
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
For n ≥ 3, the complete n‐vertex multidigraph with any fixed multiplicity of edges is proved to be decomposable into nonhamiltonian (directed) paths of arbitrarily prescribed lengths (≤ n − 2) provided that the lengths sum up to the size of the multidigraph. © 2005 Wiley Periodicals, Inc. J Graph Theory
📜 SIMILAR VOLUMES
## Abstract We prove that a 171‐edge‐connected graph has an edge‐decomposition into paths of length 3 if and only its size is divisible by 3. It is a long‐standing problem whether 2‐edge‐connectedness is sufficient for planar triangle‐free graphs, and whether 3‐edge‐connectedness suffices for graph
The proof of the following theorem is given: A complete graph with n vertkes can he decomposed into r regular bichromatic factors if and only if n is even and greater thl;iirl 4 and there exists $1 natural number k with the properties that k < r anu. ak-l < n 5 Zk.
Abstxact. The purpose of this paper is to find iI nccessar) and sufficient condition fltr the euis-trn~~ of ;L decoillposi!ion of a ~omplcte graph with given number of vc;tices into regular bichro-ma% ticfor ;uld v.1 artswcr thy' question what is the possible number of factors in such a de-c~?rnp~~i