Universality of intervals of line graph order

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Abstract

We prove that for every d ≥ 3 the homomorphism order of the class of line graphs of finite graphs with maximal degree d is universal. This means that every finite or countably infinite partially ordered set may be represented by line graphs of graphs with maximal degree d ordered by the existence of a homomorphism. © 2014.

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Fiala, J., Hubička, J., & Long, Y. (2014). Universality of intervals of line graph order. European Journal of Combinatorics, 41, 221–231. https://doi.org/10.1016/j.ejc.2014.04.008

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