An l-cycle decomposition of a graph G is said to be equitably c-colourable if there is a c-vertex-colouring of G such that each colour is represented (approximately) an equal number of times on each cycle. In this paper, we consider the existence of equitably 2-colourable even l-cycle systems of the cocktail party graph K-v - I. After establishing that the problem of proving existence of equitably 2-colourable l-cycle decompositions of K-v - I reduces to considering l-admissible values v is an element of [l, 2l), we determine a complete existence result for equitably 2-colourable l-cycle decompositions of K-v - I in the cases that v = 0,2 (mod l), or l is a power of 2, or l is an element of{2q, 4q} for q an odd prime power, or l <= 30.

Burgess, A., & Merola, F. (2021). Equitably 2-colourable even cycle systems. THE AUSTRALASIAN JOURNAL OF COMBINATORICS, 79, 437-453.

Equitably 2-colourable even cycle systems

Merola, F
2021

Abstract

An l-cycle decomposition of a graph G is said to be equitably c-colourable if there is a c-vertex-colouring of G such that each colour is represented (approximately) an equal number of times on each cycle. In this paper, we consider the existence of equitably 2-colourable even l-cycle systems of the cocktail party graph K-v - I. After establishing that the problem of proving existence of equitably 2-colourable l-cycle decompositions of K-v - I reduces to considering l-admissible values v is an element of [l, 2l), we determine a complete existence result for equitably 2-colourable l-cycle decompositions of K-v - I in the cases that v = 0,2 (mod l), or l is a power of 2, or l is an element of{2q, 4q} for q an odd prime power, or l <= 30.
Burgess, A., & Merola, F. (2021). Equitably 2-colourable even cycle systems. THE AUSTRALASIAN JOURNAL OF COMBINATORICS, 79, 437-453.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/386230
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