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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 ..."
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,3free graph with maximum degree ∆, diam(G) < ∆+64 and δ2 ≥ 9 is subpancyclic. Key words: clawfree, pancyclicity, forbidden subgraphs 1
Bounding the circumference of 3connected clawfree graphs
"... The circumference of a graph is the length of its longest cycles. A result of Jackson and Wormald implies that the circumference of a 3connected clawfree graph is at least 1 2 nlog 150 2. In this paper we improve this lower bound to Ω(n log 3 2), and our proof implies a polynomial time algorithm f ..."
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The circumference of a graph is the length of its longest cycles. A result of Jackson and Wormald implies that the circumference of a 3connected clawfree graph is at least 1 2 nlog 150 2. In this paper we improve this lower bound to Ω(n log 3 2), and our proof implies a polynomial time algorithm
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 ..."
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Cited by 12 (1 self)
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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
Strengthening the Closure Concept in ClawFree Graphs
, 1999
"... We give a strengthening of the closure concept for clawfree graphs introduced by the second author in 1997. The new closure of a clawfree graph G defined here is uniquely determined and preserves the value of the circumference of G. We present an infinite family of graphs with n vertices and 3 2 ..."
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Cited by 79 (15 self)
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We give a strengthening of the closure concept for clawfree graphs introduced by the second author in 1997. The new closure of a clawfree graph G defined here is uniquely determined and preserves the value of the circumference of G. We present an infinite family of graphs with n vertices and 3 2
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 ..."
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Cited by 1 (0 self)
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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
Clawfree graphs III. Circular interval graphs
, 2007
"... Construct a graph as follows. Take a circle, and a collection of intervals from it, no three of which have union the entire circle; take a finite set of points V from the circle; and make a graph with vertex set V in which two vertices are adjacent if they both belong to one of the intervals. Such g ..."
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Cited by 12 (5 self)
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. Such graphs are “long circular interval graphs”, and they form an important subclass of the class of all clawfree graphs. In this paper we characterize them by excluded induced subgraphs. This is a step towards the main goal of this series, to find a structural characterization of all clawfree graphs
Clawfree Graphs. III. Circular interval graphs
, 2003
"... Abstract Construct a graph as follows. Take a circle, and a collection of intervals from it, no three of which have union the entire circle; take a finite set of points V from the circle; and make a graph with vertex set V in which two vertices are adjacent if they both belong to one of the interval ..."
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of the intervals. Such graphs are "long circular interval graphs", and they form an important subclass of the class of all clawfree graphs. In this paper we characterize them by excluded induced subgraphs. This is a step towards the main goal of this series, to find a structural characterization
On Factors of 4Connected ClawFree Graphs
 J. GRAPH THEORY
, 1999
"... We consider the existence of several different kinds of factors in 4connected clawfree graphs. This is motivated by the following two conjectures which are in fact equivalent by a recent result of the third author. Conjecture 1 (Thomassen): Every 4connected line graph is hamiltonian, i.e. has ..."
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Cited by 12 (3 self)
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a connected 2factor. Conjecture 2 (Matthews and Sumner): Every 4connected clawfree graph is hamiltonian. We first show that Conjecture 2 is true within the class of hourglassfree graphs, i.e. graphs that do not contain an induced subgraph isomorphic to two triangles meeting in exactly one
Closure and Stable Hamiltonian Properties in ClawFree Graphs
, 1999
"... In the class of kconnected clawfree graphs, we study the stability of some hamiltonian properties under a closure operation introduced by the third author. We prove that (i) the properties of pancyclicity, vertex pancyclicity and cycle extendability are not stable for any k (i.e., for any of these ..."
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Cited by 16 (3 self)
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In the class of kconnected clawfree graphs, we study the stability of some hamiltonian properties under a closure operation introduced by the third author. We prove that (i) the properties of pancyclicity, vertex pancyclicity and cycle extendability are not stable for any k (i.e., for any
Forbidden Subgraphs, Hamiltonicity and Closure in ClawFree Graphs
 Discrete Math
, 1999
"... We study the stability of some classes of graphs defined in terms of forbidden subgraphs under the closure operation introduced by the second author. Using these results, we prove that every 2connected clawfree and P 7 free, or clawfree and Z 4  free, or clawfree and eiffelfree graph is ei ..."
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Cited by 7 (1 self)
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We study the stability of some classes of graphs defined in terms of forbidden subgraphs under the closure operation introduced by the second author. Using these results, we prove that every 2connected clawfree and P 7 free, or clawfree and Z 4  free, or clawfree and eiffelfree graph
Results 1  10
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20,507