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Convex p-partitions of bipartite graphs
(Elsevier, 2016)
A set of vertices X of a graph G is convex if no shortest path between two vertices in X contains a vertex outside X. We prove that for fixed p >= 1, all partitions of the vertex set of a bipartite graph into p convex sets ...
Convex Envelopes on Trees
(Heldermann Verlag, 2020-11)
We introduce two notions of convexity for an infinite regular tree. For these two notions we show that given a continuous boundary datum there exists a unique convex envelope on the tree and characterize the equation that ...
Covering graphs with convex sets and partitioning graphs into convex sets
(Elsevier Science, 2020-06)
We present some complexity results concerning the problems of covering a graph with p convex sets and of partitioning a graph into p convex sets. The following convexities are considered: digital convexity, monophonic ...
Convex and quasiconvex functions in metric graphs
(American Institute of Mathematical Sciences, 2021-12)
We study convex and quasiconvex functions on a metric graph. Given a set of points in the metric graph, we consider the largest convex function below the prescribed datum. We characterize this largest convex function as ...
Algorithms for Maximum Independent Set in Convex Bipartite Graphs
(SPRINGER, 2009)
A bipartite graph G = (V, W, E) is convex if there exists an ordering of the vertices of W such that, for each v. V, the neighbors of v are consecutive in W. We describe both a sequential and a BSP/CGM algorithm to find a ...
Toll convexity
(2015)
Formulas in connection with parameters related to convexity of paths on three vertices: caterpillars and unit interval graphs
(The University of Queensland. Combinatorial Mathematics Society of Australasia, 2021-02)
We present formulas to compute the P3 -interval number, the P3 -hull number and the percolation time for a caterpillar, in terms of certain sequences associated with it. In addition, we find a connection between the ...
Nowhere vanishing torsion closed curves always hide twice
(Kluwer Academic PublDordrechtHolanda, 1997)
Polyhedral studies on the convex recoloring problem
(ElsevierAmsterdam, 2013-11-05)
A coloring of the vertices of a graph G is convex if, for each assigned color d, the vertices with color d induce a connected subgraph of G. We address the convex recoloring problem, defined as follows. Given a graph G and ...