Sunlet factors for Cartesian products of cycles

2025/10/20 by Jervis, Henry, Kainen, Paul C.
#05C38 #05C60 #05C62 #Combinatorics (math.CO) #F.1.1 #FOS: Mathematics #G.2.2

paper · doi:10.48550/arxiv.2510.18048

Abstract

A sunlet is a cycle with a pendant edge attached at each vertex of the cycle. For the bipartite toroidal grid graphs C_2n \Box C_2n, factorizations into sunlets are given by homomorphisms from disjoint unions of s copies of a sunlet for s ∈ \1, n, n²\, n ≥ 3 such that edges are mapped bijectively.

Citations

• Decomposition of hypercubes into sunlet graphs
• Decomposition of Cartesian Product of Complete Graphs into Sunlet Graphs of Order Eight

Related

• Decomposition of Cartesian Product of Complete Graphs into Sunlet Graphs of Order Eight
• Toroidal Cartesian Products Where One Factor is 3-Connected
• Automorphisms of the canonical double cover of a toroidal grid
• A spanning union of cycles in thin cylinder, torus and Klein bottle grid graphs
• The Cartesian product of graphs with loops