Autor: |
Crespelle, Christophe, Latapy, Matthieu, Phan, Thi Ha Duong |
Rok vydání: |
2021 |
Předmět: |
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Zdroj: |
Discrete Applied Mathematics 195, 2015 |
Druh dokumentu: |
Working Paper |
DOI: |
10.1016/j.dam.2015.02.006 |
Popis: |
We 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. |
Databáze: |
arXiv |
Externí odkaz: |
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