Abstract
Given an edge-weighted tree T and two non-negative real numbers d min and d max , a pairwise compatibility graph of T for d min and d max 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 d min ≤ d T (u, v) ≤ d max in T. Here, d T (u,v) denotes the distance between u and v in T, which is the sum of the weights of the edges on the path from u to v. We call T a pairwise compatibility tree of G. We call a graph G 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 G is a pairwise compatibility graph of T for d min and d max . It is known that not all graphs are PCGs. Thus it is interesting to know which classes of graphs are PCGs. In this paper we show that triangle-free outerplanar graphs with the maximum degree 3 are PCGs.
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Salma, S.A., Rahman, M.S. (2012). Triangle-Free Outerplanar 3-Graphs Are Pairwise Compatibility Graphs. In: Rahman, M.S., Nakano, Si. (eds) WALCOM: Algorithms and Computation. WALCOM 2012. Lecture Notes in Computer Science, vol 7157. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28076-4_13
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DOI: https://doi.org/10.1007/978-3-642-28076-4_13
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