Termination of the iterated strong-factor operator on multipartite graphs

Crespelle, Christophe; Phan, Thi Ha Duong; Tran, The Hung

doi:10.1016/j.tcs.2015.01.009

Cited by 2 publications

(1 citation statement)

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“…Nevertheless, [9] recently provided an example of a graph that gives rise to an infinite factor series. This is the reason why in the next section, we constraint further the factor operation: we do not only require that the neighbourhoods of vertices at level V k−1 involved in the creation of a new vertex at level V k share at least two vertices on level V k−2 but we also require that those vertices have the same neighbourhood at level V k−3 (see Definition 7 of the clean-factor graph).…”

Section: Definition 6 (V •mentioning

confidence: 99%

On the termination of some biclique operators on multipartite graphs

Crespelle

Latapy

Phan

2015

Discrete Applied Mathematics

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International audienceWe define a new graph operator, called the weak-factor graph, which comes from the context of complex network modelling. The weak-factor operator is close to the well-known clique-graph operator but it rather operates in terms of bicliques in a multipartite graph. We address the problem of the termination of the series of graphs obtained by iteratively applying the weak-factor operator starting from a given input graph. As for the clique-graph operator, it turns out that some graphs give rise to series that do not terminate. Therefore, we design a slight variation of the weak-factor operator, called clean-factor, and prove that its associated series terminates for all input graphs. In addition, we show that the multipartite graph on which the series terminates has a very nice combinatorial structure: we exhibit a bijection between its vertices and the chains of the inclusion order on the intersections of the maximal cliques of the input graph

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Section: Definition 6 (V •mentioning

confidence: 99%