An l-cycle decomposition of K_v is said to be equitably 2-colourable if there is a 2-vertex-colouring of K_v such that each colour is represented (approximately) an equal number of times on each cycle: more precisely, we ask that in each cycle C of the decomposition, each colour appears on (l-1)/2 (floor) or (l-1)/2 (ceiling) of the vertices of C. In this paper we study the existence of equitably 2-colourable l -cycle decompositions of K_v, where l is odd, and prove the existence of such a decomposition for v=1,l (mod (2l)).
Burgess, A., Merola, F. (2024). On equitably 2-colourable odd cycle decompositions. JOURNAL OF COMBINATORIAL DESIGNS, 32(8), 419-437 [10.1002/jcd.21937].
On equitably 2-colourable odd cycle decompositions
Merola F.
2024-01-01
Abstract
An l-cycle decomposition of K_v is said to be equitably 2-colourable if there is a 2-vertex-colouring of K_v such that each colour is represented (approximately) an equal number of times on each cycle: more precisely, we ask that in each cycle C of the decomposition, each colour appears on (l-1)/2 (floor) or (l-1)/2 (ceiling) of the vertices of C. In this paper we study the existence of equitably 2-colourable l -cycle decompositions of K_v, where l is odd, and prove the existence of such a decomposition for v=1,l (mod (2l)).| File | Dimensione | Formato | |
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J of Combinatorial Designs - 2024 - Burgess - On equitably 2‐colourable odd cycle decompositions.pdf
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