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371,649
On Traceability and 2Factors in ClawFree Graphs
, 2002
"... If G is a clawfree graph of sufficiently large order n, satisfying a degree condition oe k ? n + k \Gamma 4k + 7 (where k is an arbitrary constant), then G has a 2factor with at most k \Gamma 1 components. As a second main result, we present classes of graphs C 1 ; : : : ; C 8 such that ever ..."
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such that every sufficiently large connected clawfree graph satisfying degree condition oe 6 (k) ? n+19 (or, as a corollary, ffi (G) ? n+19 ) either belongs to [ i=1 C i or is traceable.
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
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
Hamiltonian clawfree graphs
, 2005
"... A graph is clawfree if it does not have an induced subgraph isomorphic to a K1,3. In this paper, we proved the every 3connected, essentially 11connected clawfree graph is hamiltonian. We also present two related results concerning hamiltonian clawfree graphs. 1 ..."
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A graph is clawfree if it does not have an induced subgraph isomorphic to a K1,3. In this paper, we proved the every 3connected, essentially 11connected clawfree graph is hamiltonian. We also present two related results concerning hamiltonian clawfree graphs. 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 ..."
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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 ..."
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Cited by 18 (6 self)
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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
Closure concept for 2factors in clawfree graphs
, 2010
"... We introduce a closure concept for 2factors in clawfree graphs that generalizes the closure introduced by the first author. The 2factor closure of a graph is uniquely determined and the closure operation turns a clawfree graph into the line graph of a graph containing no cycles of length at most ..."
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Cited by 1 (1 self)
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We introduce a closure concept for 2factors in clawfree graphs that generalizes the closure introduced by the first author. The 2factor closure of a graph is uniquely determined and the closure operation turns a clawfree graph into the line graph of a graph containing no cycles of length
Quadrangularly connected clawfree graphs
"... A graph G is quadrangularly connected if for every pair of edges e1 and e2 in E(G), G has a sequence of lcycles (3 ≤ l ≤ 4) C1, C2,..., Cr such that e1 ∈ E(C1) and e2 ∈ E(Cr) and E(Ci) ∩ E(Ci+1) � = ∅ for i = 1, 2,..., r − 1. In this paper, we show that every quadrangularly connected clawfree gr ..."
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Cited by 1 (1 self)
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A graph G is quadrangularly connected if for every pair of edges e1 and e2 in E(G), G has a sequence of lcycles (3 ≤ l ≤ 4) C1, C2,..., Cr such that e1 ∈ E(C1) and e2 ∈ E(Cr) and E(Ci) ∩ E(Ci+1) � = ∅ for i = 1, 2,..., r − 1. In this paper, we show that every quadrangularly connected clawfree
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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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
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
of
371,649