Bi-cyclic decompositions of complete graphs into spanning trees

Dalibor Froncek

doi:10.1016/j.disc.2003.11.061

Bi-cyclic decompositions of complete graphs into spanning trees

Dalibor Froncek

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

We examine decompositions of complete graphs K_{4 k + 2} into 2 k + 1 isomorphic spanning trees. We develop a method of factorization based on a new type of vertex labelling, namely blended ρ-labelling. We also show that for every k ≥ 1 and every d, 3 ≤ d ≤ 4 k + 1 there is a tree with diameter d that decomposes K_{4 k + 2} into 2 k + 1 factors isomorphic to T.

Original language	English (US)
Pages (from-to)	1317-1322
Number of pages	6
Journal	Discrete Mathematics
Volume	307
Issue number	11-12
DOIs	https://doi.org/10.1016/j.disc.2003.11.061
State	Published - May 28 2007

Bibliographical note

Funding Information:
Research for this article was supported by the University of Minnesota Duluth Grant 177–1009.

Keywords

Graph factorization
Graph labelling
Spanning trees

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10.1016/j.disc.2003.11.061

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title = "Bi-cyclic decompositions of complete graphs into spanning trees",

abstract = "We examine decompositions of complete graphs K4 k + 2 into 2 k + 1 isomorphic spanning trees. We develop a method of factorization based on a new type of vertex labelling, namely blended ρ-labelling. We also show that for every k ≥ 1 and every d, 3 ≤ d ≤ 4 k + 1 there is a tree with diameter d that decomposes K4 k + 2 into 2 k + 1 factors isomorphic to T.",

keywords = "Graph factorization, Graph labelling, Spanning trees",

author = "Dalibor Froncek",

note = "Funding Information: Research for this article was supported by the University of Minnesota Duluth Grant 177–1009. ",

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AB - We examine decompositions of complete graphs K4 k + 2 into 2 k + 1 isomorphic spanning trees. We develop a method of factorization based on a new type of vertex labelling, namely blended ρ-labelling. We also show that for every k ≥ 1 and every d, 3 ≤ d ≤ 4 k + 1 there is a tree with diameter d that decomposes K4 k + 2 into 2 k + 1 factors isomorphic to T.

KW - Graph factorization

KW - Graph labelling

KW - Spanning trees

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ER -

Bi-cyclic decompositions of complete graphs into spanning trees

Abstract

Bibliographical note

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