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On resolvable tree-decompositions of complete graphs

✍ Scribed by Zbigniew Lonc

Publisher: John Wiley and Sons
Year: 1988
Tongue: English
Weight: 355 KB
Volume: 12
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190120219

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✦ Synopsis

A partition of the edge set of a graph H into subsets inducing graphs H,, . . . , H, isomorphic to a graph G is said to be a G-decomposition of H.

A G-decomposition of H is resolvable if the set {H,, . . . , H,} can be partitioned into subsets, called resolution classes, such that each vertex of H occurs precisely once in each resolution class. We prove that for every graceful tree T o f odd order the obvious necessary conditions for the existence of a resolvable T-decomposition of a complete graph are asymptotically sufficient. This generalizes the results of Horton and Huang concerning paths and stars.

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