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Forbidden Subgraphs, Stability and Hamiltonicity
, 1998
"... We study the stability of some classes of clawfree graphs defined in terms of forbidden subgraphs under the closure operation defined in [10]. We characterize all connected graphs A such that the class of all CAfree graphs (where C denotes the claw) is stable. Using this result, we prove that ever ..."
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Cited by 7 (3 self)
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We study the stability of some classes of clawfree graphs defined in terms of forbidden subgraphs under the closure operation defined in [10]. We characterize all connected graphs A such that the class of all CAfree graphs (where C denotes the claw) is stable. Using this result, we prove
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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; : : : ; H k (k 1) are graphs, then we say that a graph G is H 1 : : : H k free if G contains no copy of any of the graphs H 1 ; : : : ; H k as an induced subgraph; the graphs H 1 ; : : : ; H k will be also referred to in this context as forbidden subgraphs. Specifically, the fourvertex star K 1;3
Closure and Forbidden Pairs for Hamiltonicity
, 2000
"... Let C be the claw K 1;3 and N the net, i.e. the only connected graph with degree sequence 333111. It is known [Bedrossian 1991; Faudree and Gould 1997] that if X; Y is a pair of connected graphs such that, for any 2connected graph G, G being XY free implies G is hamiltonian, then X is the claw C ..."
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Cited by 3 (3 self)
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Let C be the claw K 1;3 and N the net, i.e. the only connected graph with degree sequence 333111. It is known [Bedrossian 1991; Faudree and Gould 1997] that if X; Y is a pair of connected graphs such that, for any 2connected graph G, G being XY free implies G is hamiltonian, then X is the claw C
Universal graphs with forbidden subgraphs and algebraic closure
 Advances in Applied Mathematics 22 (19
"... We apply model theoretic methods to the problem of existence of countable universal graphs with finitely many forbidden connected subgraphs. We show that to a large extent the question reduces to one of local finiteness of an associated “algebraic closure ” operator (Theorem 3, §3). The main applica ..."
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Cited by 21 (4 self)
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We apply model theoretic methods to the problem of existence of countable universal graphs with finitely many forbidden connected subgraphs. We show that to a large extent the question reduces to one of local finiteness of an associated “algebraic closure ” operator (Theorem 3, §3). The main
Closure and forbidden pairs for 2factors
, 2010
"... Pairs of connected graphs X, Y such that a graph G being 2connected and XYfree implies G is hamiltonian were characterized by Bedrossian. Using the closure concept for clawfree graphs, the first author simplified the characterization by showing that if considering the closure of G, the list in th ..."
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factor closure, the list of forbidden pairs for 2factors can be reduced to two pairs, namely, K1,4, P4 and K1,3, N1,1,3. 1 Notation and terminology In this paper, by a graph we mean a simple finite undirected graph G = (V (G), E(G)), and for notations and terminology not defined here we refer to [3
Universal graphs with a forbidden subtree
, 2006
"... 850 revision:20060524 modified:20060528 The systematic investigation of countable universal graphs with “forbidden” subgraphs was initiated in [13], followed by [12]. If C is a finite connected graph, then a graph G is Cfree if it contains no subgraph isomorphic to ..."
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Cited by 4 (2 self)
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850 revision:20060524 modified:20060528 The systematic investigation of countable universal graphs with “forbidden” subgraphs was initiated in [13], followed by [12]. If C is a finite connected graph, then a graph G is Cfree if it contains no subgraph isomorphic to
Concatenation Hierarchies and Forbidden Patterns
, 2000
"... We make the following progress on the dotdepth problem: (1) We introduce classes C B n and C L n of starfree languages defined via forbidden patterns in finite automata. It is shown for all n 0 that C B n (C L n ) contains level n + 1=2 of the dotdepth hierarchy (StraubingTherien hier ..."
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We make the following progress on the dotdepth problem: (1) We introduce classes C B n and C L n of starfree languages defined via forbidden patterns in finite automata. It is shown for all n 0 that C B n (C L n ) contains level n + 1=2 of the dotdepth hierarchy (Straubing
theomath/Workshop/WorkshopRathen.html COLORINGS 1 Vertex Colouring and Forbidden Subgraphs
"... It is not difficult to colour the vertices of a graph in polynomial time using at most ∆(G) + 1 colours, where ∆(G) denotes the maximum vertex degree of a given graph G. Moreover, the classical theorem of Brooks states that χ(G) ≤ ∆(G) unless G is a complete graph or an odd cycle. Reed [5] (see als ..."
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also [3]) believes that this result is just the tip of iceberg. He conjectured that the chromatic number is bounded by the average of the trivial upper and lower bound. Conjecture 1.1. For any graph G of maximum degree ∆, ∆ + 1 + ω χ(G) ≤ 2 The Chvatal graph [2], the smallest 4regular, triangle
SHORTEST PATHS AVOIDING FORBIDDEN SUBPATHS
, 2009
"... In this paper we study a variant of the shortest path problem in graphs: given a weighted graph G and vertices s and t, and given a set X of forbidden paths in G, find a shortest st path P such that no path in X is a subpath of P. Path P is allowed to repeat vertices and edges. We call each path ..."
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Cited by 5 (0 self)
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In this paper we study a variant of the shortest path problem in graphs: given a weighted graph G and vertices s and t, and given a set X of forbidden paths in G, find a shortest st path P such that no path in X is a subpath of P. Path P is allowed to repeat vertices and edges. We call each path
Results 1  10
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28,222