Square-free perfect graphs

Square-free perfect graphs

Optimizing Bull-Free Perfect Graphs

A bull is a graph obtained by adding a pendant vertex at two vertices of a triangle. Here we present polynomial-time combinatorial algorithms for the optimal weighted coloring and weighted clique problems in bull-free perfect graphs. The algorithms are based on a structural analysis and decomposition of bull-free perfect graphs.

Claw-free circular-perfect graphs

The circular chromatic number of a graph is a well-studied refinement of the chromatic number. Circular-perfect graphs form a superclass of perfect graphs defined by means of this more general coloring concept. This paper studies claw-free circular-perfect graphs. First we prove that ifG is a connected claw-free circular-perfect graph with χ(G) > ω(G), then min{α(G), ω(G)} = 2. We use this resu...

Square-free graphs are multiplicative

Graph homomorphism is an ubiquitous notion in graph theory with a variety of applications, and a first step to understanding more general constraints given by relational structures, see e.g. the monograph of Hell and Nešetřil [5]. We write μ : G→ H if μ is a homomorphism from the graph G to H, or simply G → H if such a homomorphism exists. For example, a graph G is k-colorable iff it has a homo...

Square-free colorings of graphs

Let G be a graph and let c be a coloring of its edges. If the sequence of colors along a walk of G is of the form a1, . . . , an, a1, . . . , an, the walk is called a square walk. We say that the coloring c is squarefree if any open walk is not a square and call the minimum number of colors needed so that G has a square-free coloring a walk Thue number and denote it by πw(G). This concept is a ...