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Eulerian disjoint paths problem in grid graphs is NPcomplete
 Discrete Applied Mathematics
, 2004
"... We show that the edge disjoint paths problem is NPcomplete in directed or undirected rectangular grids, even if the union G + H of the supply and the demand graph is Eulerian. Keywords: disjoint paths, grids, NPcompleteness 1 ..."
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We show that the edge disjoint paths problem is NPcomplete in directed or undirected rectangular grids, even if the union G + H of the supply and the demand graph is Eulerian. Keywords: disjoint paths, grids, NPcompleteness 1
Precoloring Extension on Unit Interval Graphs
, 2004
"... In the precoloring extension problem we are given a graph with some of the vertices having a preassigned color and it has to be decided whether this coloring can be extended to a proper kcoloring of the graph. Answering an open question of Hujter and Tuza [6], we show that the precoloring exten ..."
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In the precoloring extension problem we are given a graph with some of the vertices having a preassigned color and it has to be decided whether this coloring can be extended to a proper kcoloring of the graph. Answering an open question of Hujter and Tuza [6], we show that the precoloring extension problem is NPcomplete on unit interval graphs.
Approximation algorithms for edgedisjoint paths and unsplittable flow
 EFFICIENT APPROXIMATION AND ONLINE ALGORITHMS
, 2006
"... In the maximum edgedisjoint paths problem (MEDP) the input consists of a graph and a set of requests (pairs of vertices), and the goal is to connect as many requests as possible along edgedisjoint paths. We give a survey of known results about the complexity and approximability of MEDP and sketc ..."
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In the maximum edgedisjoint paths problem (MEDP) the input consists of a graph and a set of requests (pairs of vertices), and the goal is to connect as many requests as possible along edgedisjoint paths. We give a survey of known results about the complexity and approximability of MEDP and sketch some of the main ideas that have been used to obtain approximation algorithms for the problem. We consider also the generalization of MEDP where the edges of the graph have capacities and each request has a profit and a demand, called the unsplittable flow problem.
A short proof of the NPcompleteness of circular arc coloring
, 2003
"... Coloring circular arcs was shown to be NPcomplete by Garey, Johnson, Miller and Papadimitriou [5]. Here we present a simpler proof of this result. ..."
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Coloring circular arcs was shown to be NPcomplete by Garey, Johnson, Miller and Papadimitriou [5]. Here we present a simpler proof of this result.
Precoloring extension on unit interval graphs¤
, 2004
"... In the precoloring extension problem we are given a graph with some of the vertices having a preassigned color and it has to be decided whether this coloring can be extended to a proper kcoloring of the graph. Answering an open question of Hujter and Tuza [6], we show that the precoloring extensio ..."
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In the precoloring extension problem we are given a graph with some of the vertices having a preassigned color and it has to be decided whether this coloring can be extended to a proper kcoloring of the graph. Answering an open question of Hujter and Tuza [6], we show that the precoloring extension problem is NPcomplete on unit interval graphs. 1