Let (G, w ) denote a simple graph G with a weight function w : โฌ(G) -{0,1,2}. A path cover of (G, w ) is a collection of paths in G such that every edge e is contained in exactly w(e) paths of the collection. For a vertex u , w ( v ) is the sum of the weights of the edges incident with U ; U is call
Path Coverings of Graphs and Height Characteristics of Matrices
โ Scribed by D. Hershkowitz; H. Schneider
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 623 KB
- Volume
- 59
- Category
- Article
- ISSN
- 0095-8956
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๐ SIMILAR VOLUMES
## Abstract A __perfect path double cover__ (PPDC) of a graph __G__ on __n__ vertices is a family ๐ซ of __n__ paths of __G__ such that each edge of __G__ belongs to exactly two members of ๐ซ and each vertex of __G__ occurs exactly twice as an end of a path of ๐ซ. We propose and study the conjecture th
In this article, we show that for any simple, bridgeless graph G on n vertices, there is a family C of at most n-1 cycles which cover the edges of G at least twice. A similar, dual result is also proven for cocycles namely: for any loopless graph G on n vertices and edges having cogirth g \* โฅ 3 and
Seyffarth, K., Packings and perfect path double covers of maximal planar graphs, Discrete Mathematics 117 (1993) 1833195. A maximal planar graph is a simple planar graph in which every face is a triangle, and a perfect packing of such a graph by 2-cliques and facial triangles corresponds to a parti