Add to ORKGIn this text we attempt to unify many results about the K operator based on a new theory involving graphs, families and operators. We are able to build an ''operator algebra'' that helps to unify and automate arguments. In addition, we relate well-known properties, such as the Helly property, to the families and the operators. As a result, we deduce many classic results in clique graph theory from the basic fact that CS = I for conformal, reduced families. This includes Hamelink's construction, Roberts and Spencer theorem, and Ban-delt and Prisner's partial characterization of clique-fixed classes [2]. Furthermore, we show the power of our approach proving general results that lead to polynomial recognition of certain graph classes
The clique operator K maps a graph G into its clique graph, which is the intersection graph of the (...
G) = G and (G)), i > 0 and K is the clique operator. A cograph is a graph with no induced sub...
A complete set of a graph G is a subset of V inducing a complete subgraph. A clique is a maximal com...
In this text we attempt to unify many results about the K operator based on a new theory involving g...
In this text we attempt to unify many results about the K operator based on a new theory involving g...
In this text we attempt to unify many results about the K operator based on a new theory involving g...
In this text we attempt to unify many results about the K operator based on a new theory involving g...
This project is for students interested in applying algebra and computa-tion to an important problem...
Abstract. Given positive integers m, n, we consider the graphs Gn and Gm,n whose simplicial complexe...
Let P be a class of finite families of finite sets that satisfy a property P. We call ΩP the class o...
ABSTRACT. The clique polynomial of a graph is defined. An explicit formula is then derived for the c...
ABSTRACT. The clique polynomial of a graph is defined. An explicit formula is then derived for the c...
AbstractGiven positive integers m,n, we consider the graphs Gn and Gm,n whose simplicial complexes o...
This book introduces the study of algebra induced by combinatorial objects called directed graphs. T...
The clique polynomial of a graph is defined. An explicit formula is then derived for the clique poly...
The clique operator K maps a graph G into its clique graph, which is the intersection graph of the (...
G) = G and (G)), i > 0 and K is the clique operator. A cograph is a graph with no induced sub...
A complete set of a graph G is a subset of V inducing a complete subgraph. A clique is a maximal com...
In this text we attempt to unify many results about the K operator based on a new theory involving g...
In this text we attempt to unify many results about the K operator based on a new theory involving g...
In this text we attempt to unify many results about the K operator based on a new theory involving g...
In this text we attempt to unify many results about the K operator based on a new theory involving g...
This project is for students interested in applying algebra and computa-tion to an important problem...
Abstract. Given positive integers m, n, we consider the graphs Gn and Gm,n whose simplicial complexe...
Let P be a class of finite families of finite sets that satisfy a property P. We call ΩP the class o...
ABSTRACT. The clique polynomial of a graph is defined. An explicit formula is then derived for the c...
ABSTRACT. The clique polynomial of a graph is defined. An explicit formula is then derived for the c...
AbstractGiven positive integers m,n, we consider the graphs Gn and Gm,n whose simplicial complexes o...
This book introduces the study of algebra induced by combinatorial objects called directed graphs. T...
The clique polynomial of a graph is defined. An explicit formula is then derived for the clique poly...
The clique operator K maps a graph G into its clique graph, which is the intersection graph of the (...
G) = G and (G)), i > 0 and K is the clique operator. A cograph is a graph with no induced sub...
A complete set of a graph G is a subset of V inducing a complete subgraph. A clique is a maximal com...