Results 1  10
of
545,419
CliqueTransversal Sets in Cubic Graphs
, 2007
"... A cliquetransversal set S of a graph G is a set of vertices of G such that S meets all cliques of G. The cliquetransversal number, denoted τc(G), is the minimum cardinality of a cliquetransversal set in G. In this paper we present an upper bound and a lower bound on τc(G) for cubic graphs, and ch ..."
Abstract
 Add to MetaCart
A cliquetransversal set S of a graph G is a set of vertices of G such that S meets all cliques of G. The cliquetransversal number, denoted τc(G), is the minimum cardinality of a cliquetransversal set in G. In this paper we present an upper bound and a lower bound on τc(G) for cubic graphs
Pancyclicity in Clawfree Graphs
"... In this paper, we present several conditions for K1,3free graphs, which guarantee the graph is subpancyclic. In particular, we show that every K1,3free graph with minimum degree sum δ2> 2 3n+ 1 − 4; every {K1,3, P7}free graph with δ2 ≥ 9; every {K1,3, Z4}free graph with δ2 ≥ 9; and every K1,3 ..."
Abstract
 Add to MetaCart
,3free graph with maximum degree ∆, diam(G) < ∆+64 and δ2 ≥ 9 is subpancyclic. Key words: clawfree, pancyclicity, forbidden subgraphs 1
Minimal ClawFree Graphs
, 2007
"... A graph G is a minimal clawfree graph (m.c.f. graph) if it contains no K1,3 (claw) as an induced subgraph and if, for each edge e of G, G − e contains an induced claw. We investigate properties of m.c.f. graphs, establish sharp bounds on their orders and the degrees of their vertices, and character ..."
Abstract
 Add to MetaCart
A graph G is a minimal clawfree graph (m.c.f. graph) if it contains no K1,3 (claw) as an induced subgraph and if, for each edge e of G, G − e contains an induced claw. We investigate properties of m.c.f. graphs, establish sharp bounds on their orders and the degrees of their vertices
INDEPENDENCE COMPLEXES OF CLAWFREE GRAPHS
, 2005
"... We study the class of independence complexes of clawfree graphs. The main theorem give good bounds on the connectivity of these complexes, given bounds for a few subcomplexes of the same class. Two applications are presented. Firstly, we show that the independence complex of a clawfree graph with ..."
Abstract

Cited by 18 (6 self)
 Add to MetaCart
We study the class of independence complexes of clawfree graphs. The main theorem give good bounds on the connectivity of these complexes, given bounds for a few subcomplexes of the same class. Two applications are presented. Firstly, we show that the independence complex of a clawfree graph
ClawFree Graphs  a Survey.
, 1996
"... In this paper we summarize known results on clawfree graphs. The paper is subdivided into the following chapters and sections: 1. Introduction 2. Paths, cycles, hamiltonicity a) Preliminaries b) Degree and neighborhood conditions c) Local connectivity conditions d) Further forbidden subgraph ..."
Abstract

Cited by 12 (1 self)
 Add to MetaCart
In this paper we summarize known results on clawfree graphs. The paper is subdivided into the following chapters and sections: 1. Introduction 2. Paths, cycles, hamiltonicity a) Preliminaries b) Degree and neighborhood conditions c) Local connectivity conditions d) Further forbidden
TRACEABILITY IN SMALL CLAWFREE GRAPHS
"... Abstract. We prove that a clawfree, 2connected graph with fewer than 18 vertices is traceable, and we determine all nontraceable, clawfree, 2connected graphs with exactly 18 vertices and a minimal number of edges. This complements a result of Matthews on Hamiltonian graphs. 1. ..."
Abstract
 Add to MetaCart
Abstract. We prove that a clawfree, 2connected graph with fewer than 18 vertices is traceable, and we determine all nontraceable, clawfree, 2connected graphs with exactly 18 vertices and a minimal number of edges. This complements a result of Matthews on Hamiltonian graphs. 1.
ClawFree Graphs With Complete Closure
, 1999
"... We study some properties of the closure concept in clawfree graphs that was introduced by the first author. It is known that G is hamiltonian if and only if its closure is hamiltonian, but, on the other hand, there are infinite classes of nonpancyclic graphs with pancyclic closure. We show several ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
structural properties of clawfree graphs with complete closure and their clique cutsets and, using these results, we prove that every clawfree graph on n vertices with complete closure contains a cycle of length n \Gamma 1. Research supported by grant GA CR No. 201/97/0407 1 1 Introduction We refer
A Critical Point For Random Graphs With A Given Degree Sequence
, 2000
"... Given a sequence of nonnegative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n vertices of degree i. Essentially, we show that if P i(i \Gamma 2) i ? 0 then such graphs almost surely have a giant component, while if P i(i \Gamma 2) i ! 0 the ..."
Abstract

Cited by 511 (8 self)
 Add to MetaCart
Given a sequence of nonnegative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n vertices of degree i. Essentially, we show that if P i(i \Gamma 2) i ? 0 then such graphs almost surely have a giant component, while if P i(i \Gamma 2) i ! 0
Algebraic Graph Theory
"... Algebraic graph theory comprises both the study of algebraic objects arising in connection with graphs, for example, automorphism groups of graphs along with the use of algebraic tools to establish interesting properties of combinatorial objects. One of the oldest themes in the area is the investiga ..."
Abstract

Cited by 868 (12 self)
 Add to MetaCart
is the investigation of the relation between properties of a graph and the spectrum of its adjacency matrix. A central topic and important source of tools is the theory of association schemes. An association scheme is, roughly speaking, a collection of graphs on a common vertex set which fit together in a highly
Results 1  10
of
545,419