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15
Alliances in the Shadow of Conflict
, 2013
"... Victorious alliances often fight about the spoils of war. This paper presents an experiment on the determinants of whether alliances break up and fight internally after having defeated a joint enemy. First, if peaceful sharing yields an asymmetric rent distribution, this increases the likelihood of ..."
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Victorious alliances often fight about the spoils of war. This paper presents an experiment on the determinants of whether alliances break up and fight internally after having defeated a joint enemy. First, if peaceful sharing yields an asymmetric rent distribution, this increases the likelihood of fighting. In turn, anticipation of the higher likelihood of internal fight reduces the alliances ability to succeed against the outside enemy. Second, the option to make non-binding declarations on non-aggression in the relationship between alliance members does not make peaceful settlement within the alliance more likely. Third, higher differences in the alliance players' contributions to alliance effort lead to more internal
On pairwise compatibility graphs having dilworth number two
- Theoretical Compututer Science
, 2014
"... Abstract 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 d min and d max , d min ≤ d max , such that V coincides with the set of leaves of T , and there is an edge (u, v) ∈ E if a ..."
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Abstract 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 d min and d max , d min ≤ d max , such that V coincides with the set of leaves of T , and there is an edge (u, v) ∈ E if and only if is the sum of the weights of the edges on the unique path from u to v in T . When the constraints on the distance between the pairs of leaves concern only d max or only d min the two subclasses LPGs (Leaf Power Graphs) and mLPGs (minimum Leaf Power Graphs) are defined. 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. It is known that LPG ∩ mLPG is not empty and that threshold graphs, i.e. Dilworth one graphs, are contained in it. In this paper we prove that Dilworth two graphs belong to the set LPG ∩ mLPG, too. Our proof is constructive since we show how to compute all the parameters T , w, d max and d min exploiting the usual representation of Dilworth two graphs in terms of node weight function and thresholds. For graphs with Dilworth number two that are also split graphs, i.e. split permutation graphs, we provide another way to compute T , w, d min and d max when these graphs are given in terms of their intersection model.
On Graphs that are not PCGs
, 2014
"... Let T be an edge-weighted tree and let dmin; dmax be two nonnegative real numbers. The pairwise compatibility graph (PCG) of T is a graph G such that each vertex of G corresponds to a distinct leaf of T and two vertices are adjacent inG if and only if the weighted distance between their correspondin ..."
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Let T be an edge-weighted tree and let dmin; dmax be two nonnegative real numbers. The pairwise compatibility graph (PCG) of T is a graph G such that each vertex of G corresponds to a distinct leaf of T and two vertices are adjacent inG if and only if the weighted distance between their corresponding leaves in T is in the interval [dmin; dmax]. Similarly, a given graph G is a PCG if there exist suitable T; dmin; dmax, such that G is a PCG of T. Yanhaona, Bayzid and Rahman proved that there exists a graph with 15 vertices that is not a PCG. On the other hand, Calamoneri, Frascaria and Sinaimeri proved that every graph with at most seven vertices is a PCG. In this paper we
Boxicity of Leaf Powers
, 2009
"... The boxicity of a graph G, denoted as box(G) is defined as the minimum integer t such that G is an intersection graph of axisparallel t-dimensional boxes. A graph G is a k-leaf power if there exists a tree T such that the leaves of the tree correspond to the vertices of G and two vertices in G are ..."
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The boxicity of a graph G, denoted as box(G) is defined as the minimum integer t such that G is an intersection graph of axisparallel t-dimensional boxes. A graph G is a k-leaf power if there exists a tree T such that the leaves of the tree correspond to the vertices of G and two vertices in G are adjacent if and only if their corresponding leaves in T are at a distance of at most k. Leaf powers are a subclass of strongly chordal graphs and are used in the construction of phylogenetic trees in evolutionary biology. We show that for a k-leaf power G, box(G) ≤ k − 1. We also show the tightness of this bound by constructing a k-leaf power with boxicity equal to k − 1. This result implies that there exists strongly chordal graphs with arbitrarily high boxicity which is somewhat counterintuitive.
Pairwise Compatibility Graphs of Caterpillars
"... 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) is the sum of the weights of the edges on the unique path from ..."
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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) 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 concentrate our attention on PCGs for which the witness tree is a caterpillar. We first give some properties of graphs that are PCGs of a caterpillar. Then, we reformulate this problem as an integer linear programming problem and we exploit this formulation to show that for the wheels on n vertices W n , n = 7, . . . , 11, the witness tree cannot be a caterpillar. Related to this result, we conjecture that no wheel is PCG of a caterpillar. Finally, we turn our attention to PCGs of a general tree and prove that all of them admit as witness tree T a full binary tree.
Triangle-free outerplanar 3-graphs . . .
, 2013
"... A graph G = (V, E) is called a pairwise compatibility graph (P CG) if there exists an edge-weighted tree T and two non-negative real numbers dmin and dmax such that 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) ≤ dmax in T. ..."
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A graph G = (V, E) is called a pairwise compatibility graph (P CG) if there exists an edge-weighted tree T and two non-negative real numbers dmin and dmax such that 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) ≤ dmax in T. Here, dT (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. It is known that not all graphs are P CGs. Thus it is interesting to know which classes of graphs are P CGs. In this paper we show that triangle-free outerplanar graphs with the maximum degree 3 are PCGs.
Research Area Markets and Choice
, 2013
"... www.wzb.eu Copyright remains with the authors. Discussion papers of the WZB serve to disseminate the research results of work in progress prior to publication to encourage the exchange of ideas and academic debate. Inclusion of a paper in the discussion paper series does not constitute publication a ..."
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www.wzb.eu Copyright remains with the authors. Discussion papers of the WZB serve to disseminate the research results of work in progress prior to publication to encourage the exchange of ideas and academic debate. Inclusion of a paper in the discussion paper series does not constitute publication and should not limit publication in any other venue. The discussion papers published by the WZB represent the views of the respective author(s) and not of the institute as a whole. Affiliation of the authors:
