Let (G, w ) denote a simple graph G with a weight function w : €(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
Identifying path covers in graphs
✍ Scribed by Foucaud, Florent; Kovše, Matjaž
- Book ID
- 121929386
- Publisher
- Elsevier Science
- Year
- 2013
- Tongue
- English
- Weight
- 417 KB
- Volume
- 23
- Category
- Article
- ISSN
- 1570-8667
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## Abstract A __perfect path double cover__ (PPDC) of a graph __G__ on __n__ vertices is a family 𝒫 of __n__ paths of __G__ such that each edge of __G__ belongs to exactly two members of 𝒫 and each vertex of __G__ occurs exactly twice as an end of a path of 𝒫. We propose and study the conjecture th
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