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Subcubic trianglefree graphs have fractional chromatic number at most 14/5
, 2013
"... We prove that every subcubic trianglefree graph has fractional chromatic number at most 14/5, thus confirming a conjecture of Heckman and Thomas [A new proof of the independence ratio of trianglefree cubic graphs. Discrete Math. 233 (2001), 233–237]. ..."
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Cited by 4 (1 self)
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We prove that every subcubic trianglefree graph has fractional chromatic number at most 14/5, thus confirming a conjecture of Heckman and Thomas [A new proof of the independence ratio of trianglefree cubic graphs. Discrete Math. 233 (2001), 233–237].
The fractional chromatic number of trianglefree graphs with ∆ ≤ 3
, 2010
"... Let G be any trianglefree graph with maximum degree ∆ ≤ 3. Staton 5 proved that the independence number of G is at least n. Heckman 14 and Thomas conjectured that Staton’s result can be strengthened into a bound on the fractional chromatic number of G, namely χf(G) ≤ 14 5.. In this paper, we prov ..."
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Cited by 6 (2 self)
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Let G be any trianglefree graph with maximum degree ∆ ≤ 3. Staton 5 proved that the independence number of G is at least n. Heckman 14 and Thomas conjectured that Staton’s result can be strengthened into a bound on the fractional chromatic number of G, namely χf(G) ≤ 14 5.. In this paper, we
Books in graphs
, 2008
"... A set of q triangles sharing a common edge is called a book of size q. We write β (n, m) for the the maximal q such that every graph G (n, m) contains a book of size q. In this note 1) we compute β ( n, cn 2) for infinitely many values of c with 1/4 < c < 1/3, 2) we show that if m ≥ (1/4 − α) ..."
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Cited by 2380 (22 self)
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A set of q triangles sharing a common edge is called a book of size q. We write β (n, m) for the the maximal q such that every graph G (n, m) contains a book of size q. In this note 1) we compute β ( n, cn 2) for infinitely many values of c with 1/4 < c < 1/3, 2) we show that if m ≥ (1/4 − α
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices
Trianglefree subcubic graphs with minimum bipartite density
 J. Combin. Theory Ser. B
"... A graph is subcubic if its maximum degree is at most 3. The bipartite density of a graph G is max{ε(H)/ε(G) : H is a bipartite subgraph of G}, where ε(H) and ε(G) denote the numbers of edges in H and G, respectively. It is an NPhard problem to determine the bipartite density of any given trianglef ..."
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Cited by 7 (2 self)
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A graph is subcubic if its maximum degree is at most 3. The bipartite density of a graph G is max{ε(H)/ε(G) : H is a bipartite subgraph of G}, where ε(H) and ε(G) denote the numbers of edges in H and G, respectively. It is an NPhard problem to determine the bipartite density of any given trianglefree
The trianglefree 2matching polytope of subcubic graphs
, 2012
"... The trianglefree 2matching polytope of subcubic graphs⋆ Kristóf Bérczi⋆⋆ Abstract: The problem of determining the maximum size of a Ckfree 2matching (that is, a 2matching not containing cycles of length k) is a much studied question of matching theory. Cornuéjols and Pulleyblank showed that dec ..."
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The trianglefree 2matching polytope of subcubic graphs⋆ Kristóf Bérczi⋆⋆ Abstract: The problem of determining the maximum size of a Ckfree 2matching (that is, a 2matching not containing cycles of length k) is a much studied question of matching theory. Cornuéjols and Pulleyblank showed
A fast and high quality multilevel scheme for partitioning irregular graphs
 SIAM JOURNAL ON SCIENTIFIC COMPUTING
, 1998
"... Recently, a number of researchers have investigated a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph [Bui and Jones, Proc. ..."
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Cited by 1173 (16 self)
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Recently, a number of researchers have investigated a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph [Bui and Jones, Proc.
Results 1  10
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55,633