en
A 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.
https://scigraph.springernature.com/explorer/license/
2019-04-15T17:11
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http://link.springer.com/10.1007/978-3-642-28076-4_14
chapter
On Relaxing the Constraints in Pairwise Compatibility Graphs
chapters
2012-01-01
124-135
2012
Medical and Health Sciences
Springer Berlin Heidelberg
Berlin, Heidelberg
0deb7f9e3eb5ae2a9f26d2c51019b958374b684160d9f6f618a5c4ef2f75fd44
readcube_id
doi
10.1007/978-3-642-28076-4_14
Sapienza University of Rome
Department of Computer Science, “Sapienza” University of Rome, Italy, via Salaria 113, 00198 Roma
Shin-ichi
Nakano
Tiziana
Calamoneri
Sinaimeri
Blerina
Neurosciences
Springer Nature - SN SciGraph project
Rahman
Md. Saidur
978-3-642-28076-4
WALCOM: Algorithms and Computation
978-3-642-28075-7
Rossella
Petreschi
dimensions_id
pub.1002922678