## Abstract We prove in this paper that every simple graph __G__ admits a perfect path double cover (PPDC), i.e., a set of paths of __G__ such that each edge of __G__ belongs to exactly two of the paths and each vertex of __G__ is an end of exactly two of the paths, where a path of length zero is c
Perfect double covers with paths of length four
β Scribed by Heinrich, K.; Horak, P.; Wallis, W.; Yu, Qinglin
- Publisher
- John Wiley and Sons
- Year
- 1996
- Tongue
- English
- Weight
- 347 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0364-9024
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β¦ Synopsis
It is shown that for any 4-regular graph G there is a collection F of paths of length 4 such that each edge of G belongs to exactly two of the paths and each vertex of G occurs exactly twice as an endvertex of a path of y. This proves a special case of a conjecture of Bondy. 0 1996 John Wiley & Sons, Inc.
π SIMILAR VOLUMES
## Abstract Bondy conjectured that every simple bridgeless graph has a small cycle double cover (SCDC). We show that this is the case for the lexicographic products of certain graphs and along the way for the Cartesian product as well. Specifically, if __G__ does not have an isolated vertex then __
## Abstract A double Dudeney set in __K~n~__ is a multiset of Hamilton cycles in __K~n~__ having the property that each 2βpath in __K~n~__ lies in exactly two of the cycles. A double Dudeney set in __K~n~__ has been constructed when __n__ββ₯β4 is even. In this paper, we construct a double Dudeney se
An induced path-cycle double cover (IPCDC) of a simple graph G is a family F Γ {F 1 , . . . , F k } of induced paths and cycles of G such that if F i Κ F j x M, then F i Κ F j is a vertex or an edge, for i x j, each edge of G appears in precisely two of the F i 's, and each vertex of G appears in pr
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