The problem of the edge coloring partial k-tree into two partial p-and q-trees with p, q Γ΅ k is considered. An algorithm is provided to construct such a coloring with p / q Γ k. Usefulness of this result in a Lagrangian decomposition framework to solve certain combinatorial optimization problems is
A comparison of two edge-coloring formulations
β Scribed by Jon Lee; Janny Leung
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 497 KB
- Volume
- 13
- Category
- Article
- ISSN
- 0167-6377
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Bounds are given on the number of colors required to color the edges of a graph (multigraph) such that each color appears at each vertex u at most m(u) times. The known results and proofs generalize in natural ways. Certain new edge-coloring problems, which have no counterparts when m(u) = 1 for all
## Abstract We investigate the conjecture that a graph is perfect if it admits a twoβedgeβcoloring such that two edges receive different colors if they are the nonincident edges of a __P__~4~ (chordless path with four vertices). Partial results on this conjecture are given in this paper. Β© 1995 Joh
Certain problems involving the coloring the edges or vertices of infinite graphs are shown to be undecidable. In particular, let G and H be finite 3-connected graphs, or triangles. Then a doubly-periodic infinite graph F is constructed such that the following problem is undecidable: For a coloring o
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