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Split-critical and uniquely split-colorable graphs

Publications associées (41)

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Coloring some classes of mixed graphs

Bernard Ries

We consider the coloring problem for mixed graphs, that is, for graphs containing edges and arcs. A mixed coloring

c

is a coloring such that for every edge

[x_{i},x_{j}]

c(x_{i})\neq c(x_{j})

and for every arc

(x_{p},x_{q})

, $c(x_{p})

2007

Bicolored matchings in some classes of graphs

Dominique de Werra, Bernard Ries

We consider the problem of finding in a graph a set

R

of edges to be colored in red so that there are maximum matchings having some prescribed numbers of red edges. For regular bipartite graphs with

n

nodes on each side, we give sufficient conditions f ...

2007

Generalized vertex coloring problems using split graphs

Tinaz Ekim

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. ...

EPFL2006

Variations of split-coloring in permutation graphs

Dominique de Werra, Tinaz Ekim

Combinatorial optimization problems related to permutations have been widely studied. Here, we consider different generalizations of the usual coloring problem in permutation graphs. A cocoloring is a partition of a permutation into increasing and decreasi ...

2006

Polar cographs

Dominique de Werra, Tinaz Ekim

Polar graphs are a natural extension of some classes of graphs like bipartite graphs, split graphs and complements of bipartite graphs. A graph is (s,k)-polar if there exists a partition A,B of its vertex set such that A induces a complete s-partite graph ...

2005

Partitioning cographs into cliques and stable sets

Dominique de Werra, Tinaz Ekim

We consider the problem of partitioning the node set of a graph into p cliques and k stable sets, namely the (p,k)-coloring problem. Results have been obtained for general graphs \cite{hellcomp}, chordal graphs \cite{hellchordal} and cacti for the case whe ...

2005

On the stable set polytope of claw-free graphs

Gautier Stauffer

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 ...

EPFL2005

Suboptimal colorings and solution of large chromatic scheduling problems

Ivo Blöchliger

Graph Coloring is a very active field of research in graph theory as well as in the domain of the design of efficient heuristics to solve problems which, due to their computational complexity, cannot be solved exactly (no guarantee that an optimal solution ...

EPFL2005

Circular Ones Matrices and the Stable Set Polytope of Quasi-Line Graphs

Friedrich Eisenbrand, Gautier Stauffer

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 ...

2004

Fully dynamic cycle-equivalence in graphs

Monika Henzinger

Two edges e_1 and e_2 of an undirected graph are cycle-equivalent iff all cycles that contain e_1 also contain e_2, i.e., iff e_1 and e_2 are a cut-edge pair. The cycle-equivalence classes of the control-flow graph are used in optimizing compilers to speed ...

1994