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96
Contractible Subgraphs in kConnected Graphs
, 2006
"... For a graph G we define a graph T(G) whose vertices are the triangles in G and two vertices of T(G) are adjacent if their corresponding triangles in G share an edge. Kawarabayashi showed that if G is a kconnected graph and T(G) contains no edge then G admits a kcontractible clique of size at most ..."
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For a graph G we define a graph T(G) whose vertices are the triangles in G and two vertices of T(G) are adjacent if their corresponding triangles in G share an edge. Kawarabayashi showed that if G is a kconnected graph and T(G) contains no edge then G admits a kcontractible clique of size at most
Contractible subgraphs and Morita equivalence of graph C
 algebras, Proc. Amer. Math. Soc
"... Abstract. In this paper we describe an operation on directed graphs which produces a graph with fewer vertices, such that the C ∗algebra of the new graph is Morita equivalent to that of the original graph. We unify and generalize several related constructions, notably delays and desingularizations ..."
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Cited by 6 (1 self)
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Abstract. In this paper we describe an operation on directed graphs which produces a graph with fewer vertices, such that the C ∗algebra of the new graph is Morita equivalent to that of the original graph. We unify and generalize several related constructions, notably delays and desingularizations of directed graphs. 1.
Contractible subgraphs, Thomassen’s conjecture and the Dominating Cycle Conjecture in snarks
, 2007
"... We show that the conjectures by Matthews and Sumner (every 4connected clawfree graph is hamiltonian), by Thomassen (every 4connected line graph is hamiltonian) and by Fleischner (every cyclically 4edgeconnected cubic graph has either a 3edgecoloring or a dominating cycle), which are known to b ..."
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Cited by 2 (2 self)
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to be equivalent, are equivalent with the statement that every snark (i.e. a cyclically 4edgeconnected cubic graph of girth at least five that is not 3edgecolorable) has a dominating cycle. We use a refinement of the contractibility technique which was introduced by Ryjáček and Schelp in 2003 as a common
Contracting Few Edges to Remove Forbidden Induced Subgraphs
"... Abstract. For a given graph property Π (i.e., a collection Π of graphs), the ΠContraction problem is to determine whether the input graph G can be transformed into a graph satisfying property Π by contracting at most k edges, where k is a parameter. In this paper, we mainly focus on the parameteriz ..."
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Cited by 2 (1 self)
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on the parameterized complexity of ΠContraction problems for Π being Hfree (i.e., containing no induced subgraph isomorphic to H) for various fixed graphs H. We show that Clique Contraction (equivalently, P3Free Contraction for connected graphs) is FPT (fixedparameter tractable) but admits no polynomial kernel
Forbidden Induced Subgraph Characterization of Cograph Contraction
 J. GRAPH THEORY
, 2001
"... We solve the problem of characterization of cograph contraction. Let P be a hereditary class proposed by Le [2]. ..."
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Cited by 1 (0 self)
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We solve the problem of characterization of cograph contraction. Let P be a hereditary class proposed by Le [2].
On Maximum Symmetric Subgraphs
 Proc. of Graph Drawing 2000, Lecture Notes in Computer Science
, 2001
"... Let G be an nnode graph. We address the problem of computing a maximum symmetric graph H from G by deleting nodes, deleting edges, and contracting edges. This NPcomplete problem arises naturally from the objective of drawing G as symmetrically as possible. We show that its tractability for the spe ..."
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Cited by 8 (1 self)
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Let G be an nnode graph. We address the problem of computing a maximum symmetric graph H from G by deleting nodes, deleting edges, and contracting edges. This NPcomplete problem arises naturally from the objective of drawing G as symmetrically as possible. We show that its tractability
Tensor networks and the enumeration of regular subgraphs
"... Abstract. We propose a universal approach to a range of enumeration problems in graphs. The key point is in contracting suitably chosen symmetric tensors placed at the vertices of a graph along the edges. In particular, this leads to an algorithm that counts the number of dregular subgraphs of an a ..."
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Cited by 3 (0 self)
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Abstract. We propose a universal approach to a range of enumeration problems in graphs. The key point is in contracting suitably chosen symmetric tensors placed at the vertices of a graph along the edges. In particular, this leads to an algorithm that counts the number of dregular subgraphs
Eulerian Subgraphs in Graphs with Short Cycles
"... P. Paulraja recently showed that if every edge of a graph G lies in a cycle of length at most 5 and if G has no induced K1,3 as a subgraph, then G has a spanning closed trail. We use a weaker hypothesis to obtain a stronger conclusion. We also give a related sufficient condition for the existence of ..."
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Cited by 2 (2 self)
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and Y by X△Y. A graph is called eulerian if it is connected and its vertices have even degree. For any graph G and any edge e ∈ E(G), we let G/e denote the graph obtained from G by contracting e and by deleting any resulting loops. If H is a connected subgraph of G, then G/H denotes the graph obtained
THE ENUMERATION OF VERTEX INDUCED SUBGRAPHS WITH RESPECT TO THE NUMBER OF COMPONENTS
, 2009
"... Inspired by the study of community structure in connection networks, we introduce the graph polynomial Q (G; x, y), the bivariate generating function which counts the number of connected components in induced subgraphs. We give a recursive definition of Q (G; x, y) using vertex deletion, vertex con ..."
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Cited by 10 (0 self)
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Inspired by the study of community structure in connection networks, we introduce the graph polynomial Q (G; x, y), the bivariate generating function which counts the number of connected components in induced subgraphs. We give a recursive definition of Q (G; x, y) using vertex deletion, vertex
Results 1  10
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96