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EnglishA graph G is called a pairwise compatibility graph (PCG) if there exists an edge weighted tree T and two non-negative real numbers d min and d max such that each leaf l u of T corresponds to a vertex u ∈ V and there is an edge (u,v) ∈ E if and only if d min ≤ d T (l u, l v ) ≤ d max where d T (l u, l v ) is the sum of the weights of the edges on the unique path from l u to l v in T. In this paper we analyze the class of PCG in relation with two particular subclasses resulting from the the cases where d min = 0 (LPG) and d max = + ∞ (mLPG). In particular, we show that the union of LPG and mLPG does not coincide with the whole class PCG, their intersection is not empty, and that neither of the classes LPG and mLPG is contained in the other. Finally, as the graphs we deal with belong to the more general class of split matrogenic graphs, we focus on this class of graphs for which we try to establish the membership to the PCG class. © 2012 Springer-Verlag.
On relaxing the constraints in pairwise compatibility graphs / Calamoneri, Tiziana; Petreschi, Rossella; Sinaimeri, Blerina. - STAMPA. - 7157 LNCS(2012), pp. 124-135. ((Intervento presentato al convegno 6th International Workshop on Algorithms and Computation, WALCOM 2012 tenutosi a Dhaka nel 15 February 2012 through 17 February 2012.
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| Titolo: | On relaxing the constraints in pairwise compatibility graphs |
| Autori: | |
| Data di pubblicazione: | 2012 |
| Serie: | |
| Citazione: | On relaxing the constraints in pairwise compatibility graphs / Calamoneri, Tiziana; Petreschi, Rossella; Sinaimeri, Blerina. - STAMPA. - 7157 LNCS(2012), pp. 124-135. ((Intervento presentato al convegno 6th International Workshop on Algorithms and Computation, WALCOM 2012 tenutosi a Dhaka nel 15 February 2012 through 17 February 2012. |
| Handle: | http://hdl.handle.net/11573/442904 |
| ISBN: | 9783642280757 9783642280764 |
| Appartiene alla tipologia: | 04b Atto di convegno in volume |
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