On Decompositions of K18k and K18k+1 into Certain Connected Bicyclic Graphs with Nine Edges

Ryan C. Bunge; Dalibor Froncek; Andrew Sailstad

doi:10.61091/um119-05

On Decompositions of K_18k and K_18k+1 into Certain Connected Bicyclic Graphs with Nine Edges

Ryan C. Bunge, Dalibor Froncek, Andrew Sailstad

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

Abstract

We show that connected, bicyclic graphs on nine edges with at least one cycle other than C₃ decompose the complete graphs K_18k and K₁₈k₊₁, for k ≥ 1, when the necessary conditions allow for such a decomposition. This complements previous results by Freyberg, Froncek, Jeffries, Jensen, and Sailstad on connected bicyclic triangular graphs.

Original language	English (US)
Pages (from-to)	37-49
Number of pages	13
Journal	Utilitas Mathematica
Volume	119
Issue number	1
DOIs	https://doi.org/10.61091/um119-05
State	Published - 2024
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2024 Utilitas Mathematica Publishing Inc.. All rights reserved.

Keywords

Graph decompositions
Tripartite graphs
ρ-labelings

Publisher link

10.61091/um119-05

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abstract = "We show that connected, bicyclic graphs on nine edges with at least one cycle other than C3 decompose the complete graphs K18k and K18k+1, for k ≥ 1, when the necessary conditions allow for such a decomposition. This complements previous results by Freyberg, Froncek, Jeffries, Jensen, and Sailstad on connected bicyclic triangular graphs.",

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