Some Results on Chromaticity of Quasi-Linear Paths and Cycles
Keywords:
Quasi-linear hypergraph, Sunflower hypergraph, Quasi-linear path, Quasi-linear cycle, Chromatic polynomial, Chromatic uniqueness, Potential function
Abstract
Let r≥1 be an integer. An h-hypergraph H is said to be r-quasi-linear (linear for r=1) if any two edges of H intersect in 0 or r vertices. In this paper it is shown that r-quasi-linear paths Ph,rm of length m≥1 and cycles Ch,rm of length m≥3 are chromatically unique in the set of h-uniform r-quasi-linear hypergraphs provided r≥2 and h≥3r−1.