Abstract
Let r ≥ 1 be an integer. An h-hypergraph H is said to be r-quasilinear (linear for r = 1) if any two edges of H intersect in 0 or r vertices. This paper surveys chromaticity of r-quasilinear h-hypergraphs with emphasis to sunflower hypergraphs SH(n, p, h), r-quasilinear paths P m h, r of length m ≥ 1, and cycles C m h, r of length m ≥ 3. They are chromatically unique in the set of h-uniform hypergraphs provided 1 ≤ p ≤ h − 2, or \(p = h - 1\) and they have at most two edges, and in the set of h-uniform r-quasilinear hypergraphs if r ≥ 2 and h ≥ 3r − 1, respectively.
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Tomescu, I. (2015). Some Results on Chromaticity of Quasilinear Hypergraphs. In: Cartier, P., Choudary, A., Waldschmidt, M. (eds) Mathematics in the 21st Century. Springer Proceedings in Mathematics & Statistics, vol 98. Springer, Basel. https://doi.org/10.1007/978-3-0348-0859-0_12
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DOI: https://doi.org/10.1007/978-3-0348-0859-0_12
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