Removing and Adding Edges for the Traveling Salesman Problem
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We show that every graph G with maximum degree three has a straight-line drawing in the plane using edges of at most five different slopes. Moreover, if G is connected and has at least one vertex of degree less than three, then four directions suffice. ...
Graph theory experienced a remarkable increase of interest among the scientific community during the last decades. The vertex coloring problem (Min Coloring) deserves a particular attention rince it has been able to capture a wide variety of applications. ...
We are interested in coloring the vertices of a mixed graph, i.e., a graph containing edges and arcs. We consider two different coloring problems: in the first one we want adjacent vertices to have different colors and the tail of an arc to get a color str ...
In this thesis we focus our attention on the stable set polytope of claw-free graphs. This problem has been open for many years and albeit all the efforts engaged during those last three years, it is still open. This does not mean that no progress has been ...
It is a long standing open problem to find an explicit description of the stable set polytope of claw-free graphs. Yet more than 20 years after the discovery of a polynomial algorithm for the maximum stable set problem for claw-free graphs, there is even n ...
We deal with non-rank facets of the stable set polytope of claw-free graphs. We extend results of Giles and Trotter [7] by (i) showing that for any nonnegative integer a there exists a circulant graph whose stable set polytope has a facet-inducing inequali ...
It is a long standing open problem to find an explicit description of the stable set polytope of claw-free graphs. Yet more than 20 years after the discovery of a polynomial algorithm for the maximum stable set problem for claw-free graphs, there is even n ...
The graph coloring problem is one of the most famous problems in graph theory and has a large range of applications. It consists in coloring the vertices of an undirected graph with a given number of colors such that two adjacent vertices get different col ...
It is a long standing open problem to find an explicit description of the stable set polytope of claw-free graphs. Yet more than 20 years after the discovery of a polynomial algorithm for the maximum stable set problem for claw-free graphs, there is even n ...