On pairwise compatibility graphs having Dilworth number k
نویسندگان
چکیده
منابع مشابه
On pairwise compatibility graphs having Dilworth number two
A graph G = (V, E) is called a pairwise compatibility graph (PCG) if there exists a tree T , a positive edge-weight function w on T , and two non-negative real numbers dmin and dmax, dmin ≤ dmax, such that V coincides with the set of leaves of T , and there is an edge (u, v) ∈ E if and only if dmin ≤ dT,w(u, v) ≤ dmax where dT,w(u, v) is the sum of the weights of the edges on the unique path fr...
متن کاملOn Dilworth k Graphs and Their Pairwise Compatibility
The Dilworth number of a graph is the size of the largest subset of its nodes in which the close neighborhood of no node contains the neighborhood of another one. In this paper we give a new characterization of Dilworth k graphs, for each value of k, exactly defining their structure. Moreover, we put these graphs in relation with pairwise compatibility graphs (PCGs), i.e. graphs on n nodes that...
متن کاملGraphs with Dilworth Number Two are Pairwise Compatibility Graphs
A graph G = (V, E) is called a pairwise compatibility graph (PCG) if there exists a tree T , a positive edge-weight function w on T , and two non-negative real numbers dmin and dmax, dmin ≤ dmax, such that V coincides with the set of leaves of T , and there is an edge (u, v) ∈ E if and only if dmin ≤ dT,w(u, v) ≤ dmax where dT,w(u, v) is the sum of the weights of the edges on the unique path fr...
متن کاملCorrigendum to "On pairwise compatibility graphs having Dilworth number two" [Theoret. Comput. Science (2014) 34-40]
In [4] we put in relation graphs with Dilworth number at most two and the two classes LPG and mLPG. In order to prove this relation, we have heavily exploited a result we deduced from [1]. We have now realized that this result is not always true, so in this corrigendum we correctly restate the result concerning the relation between graphs with Dilworth number at most two and the two classes of ...
متن کاملPairwise Compatibility Graphs
Let T be an edge weighted tree, let dT (u, v) be the sum of the weights of the edges on the path from u to v in T , and let dmin and dmax be two non-negative real numbers such that dmin ≤ dmax. Then a pairwise compatibility graph of T for dmin and dmax is a graph G = (V, E), where each vertex u ∈ V corresponds to a leaf u of T and there is an edge (u, v) ∈ E if and only if dmin ≤ dT (u, v) ≤ dm...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2014
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2014.06.024