Packings and perfect path double covers of maximal planar graphs
نویسندگان
چکیده
منابع مشابه
On eulerian and regular perfect path double covers of graphs
A perfect path double cover (PPDC) of a graph G is a family P of paths of G such that every edge of G belongs to exactly two paths of P and each vertex of G occurs exactly twice as an endpoint of a path in P. Li (J. Graph Theory 14 (1990) 645–650) has shown that every simple graph has a PPDC.A regular perfect path double cover (RPPDC) of a graph G is a PPDC of G in which all paths are of the sa...
متن کاملPath decompositions and perfect path double covers
We consider edge-decompositions of regular graphs into isomorphic paths. An m-PPD (perfect path decomposition) is a decomposition of a graph into paths of length m such that every vertex is an end of exactly two paths. An m-PPDC (perfect path double cover) is a covering of the edges by paths of length m such that every edge is covered exactly two times and every vertex is an end of exactly two ...
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Planar locally finite graphs which are almost vertex transitive are discussed. If the graph is 3-connected and has at most one end then the group of automorphisms is a planar discontinuous group and its structure is wellknown. A general result is obtained for such graphs where no restriction is put on the number of ends. It is shown that such a graph can be built up from one-ended or finite pla...
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A set P of disjoint paths in a graph G is called a (complete) path cover of G if every vertex of G belongs to one of the paths in P. A path cover of any subgraph of G is called a partial path cover of G. For xed k > 0, a k-blanket of graph G is a partial path cover P of G, consisting of exactly k paths, that maximizes the size of the subgraph covered by P. A k-core of graph G is a partial path ...
متن کاملIdentifying path covers in graphs
This paper introduces the problem of identifying vertices of a graph using paths. An identifying path cover of a graph G is a set P of paths such that each vertex belongs to a path of P, and for each pair u, v of vertices, there is a path of P which includes exactly one of u, v. This new notion is related to a large number of other identi cation problems in graphs and hypergraphs. We study the ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1993
ISSN: 0012-365X
DOI: 10.1016/0012-365x(93)90334-p