The micro-world of cographs

Alecu, Bogdan; Werra, Dominique de

doi:10.1016/j.dam.2021.11.004

Cited by 5 publications

(1 citation statement)

References 45 publications

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“…In fact, as we show in Theorem 10 below, those three classes are the only minimal classes of unbounded h-index. We note that a "prototype" of this characterisation appeared in [3], where the set of minimal classes of unbounded h-index was identified within the class of cographs. It was also conjectured in [3] that this characterisation extends to the universe of all graphs, which is what we now show.…”

Section: H-indexmentioning

confidence: 93%

Graph parameters, implicit representations and factorial properties

Alecu¹,

Alekseev²,

Atminas³

et al. 2023

Preprint

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How to efficiently represent a graph in computer memory is a fundamental data structuring question. In the present paper, we address this question from a combinatorial point of view. A representation of an n-vertex graph G is called implicit if it assigns to each vertex of G a binary code of length O(log n) so that the adjacency of two vertices is a function of their codes. A necessary condition for a hereditary class X of graphs to admit an implicit representation is that X has at most factorial speed of growth. This condition, however, is not sufficient, as was recently shown in [Hatami & Hatami, FOCS 2022]. Several sufficient conditions for the existence of implicit representations deal with boundedness of some parameters, such as degeneracy or clique-width. In the present paper, we analyze more graph parameters and prove a number of new results related to implicit representation and factorial properties.

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Section: H-indexmentioning

confidence: 93%