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1,203
On Hypergraphs of Girth Five
 ELECTRONIC JOURNAL OF COMBINATORICS
, 2003
"... In this paper, we study runiform hypergraphs without cycles of length less than five, employing the definition of a hypergraph cycle due to Berge. In particular, for r = 3, we show that if has n vertices and a maximum number of edges, then 1 ). This also asymptotically determines the gene ..."
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Cited by 12 (4 self)
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In this paper, we study runiform hypergraphs without cycles of length less than five, employing the definition of a hypergraph cycle due to Berge. In particular, for r = 3, we show that if has n vertices and a maximum number of edges, then 1 ). This also asymptotically determines
Generalized Girth Problems in Graphs and Hypergraphs
, 2013
"... We study the asymptotic value of several extremal problems on graphs and hypergraphs, that arise as generalized notions of girth. Apart from being combinatorially natural questions, they are motivated by computationaltheoretic applications. 1. An `subgraph is a subgraph with ` edges per vertex, or ..."
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We study the asymptotic value of several extremal problems on graphs and hypergraphs, that arise as generalized notions of girth. Apart from being combinatorially natural questions, they are motivated by computationaltheoretic applications. 1. An `subgraph is a subgraph with ` edges per vertex
On Groupoids and Hypergraphs
, 2012
"... We present a novel construction of finite groupoids whose Cayley graphs have large girth even w.r.t. a discounted distance measure that contracts arbitrarily long sequences of edges from the same colour class (subgroupoid), and only counts transitions between colour classes (cosets). These groupoi ..."
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Cited by 3 (3 self)
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We present a novel construction of finite groupoids whose Cayley graphs have large girth even w.r.t. a discounted distance measure that contracts arbitrarily long sequences of edges from the same colour class (subgroupoid), and only counts transitions between colour classes (cosets
Colouring planar mixed hypergraphs
 ELECTRONIC J. COMBIN
, 2000
"... A mixed hypergraph is a triple H =(V,C, D) where V is the vertex set and C and D are families of subsets of V,theCedges and Dedges, respectively. A kcolouring of H is a mapping c: V → [k] such that each Cedge has at least two vertices with a Common colour and each Dedge has at least two vertice ..."
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Cited by 17 (1 self)
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A mixed hypergraph is a triple H =(V,C, D) where V is the vertex set and C and D are families of subsets of V,theCedges and Dedges, respectively. A kcolouring of H is a mapping c: V → [k] such that each Cedge has at least two vertices with a Common colour and each Dedge has at least two
Constructions for Cubic Graphs With Large Girth
 Electronic Journal of Combinatorics
, 1998
"... The aim of this paper is to give a coherent account of the problem of constructing cubic graphs with large girth. There is a welldefined integer ¯ 0 (g), the smallest number of vertices for which a cubic graph with girth at least g exists, and furthermore, the minimum value ¯ 0 (g) is attained by a ..."
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Cited by 53 (1 self)
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The aim of this paper is to give a coherent account of the problem of constructing cubic graphs with large girth. There is a welldefined integer ¯ 0 (g), the smallest number of vertices for which a cubic graph with girth at least g exists, and furthermore, the minimum value ¯ 0 (g) is attained
The Uniformity Space of Hypergraphs and its Applications
"... Let H = (V; E) be a hypergraph, and let F be a field. A function f : V ! F is called stable if for each e 2 E, the sum of the values of f on the members of e is the same. The linear space consisting of the stable functions, denoted by U (H; F ), is called the uniformity space of H over F . The di ..."
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Cited by 1 (0 self)
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Let H = (V; E) be a hypergraph, and let F be a field. A function f : V ! F is called stable if for each e 2 E, the sum of the values of f on the members of e is the same. The linear space consisting of the stable functions, denoted by U (H; F ), is called the uniformity space of H over F
On the number of edges in hypergraphs critical with respect to strong colourings
 European Journal of Combinatorics
"... A colouring of the vertices of a hypergraph G is called strong if, for every edge A, the colours of all vertices in A are distinct. It corresponds to a colouring of the generated graph Ɣ(G) obtained from G by replacing every edge by a clique. We estimate the minimum number of edges possible in a kc ..."
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Cited by 1 (1 self)
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A colouring of the vertices of a hypergraph G is called strong if, for every edge A, the colours of all vertices in A are distinct. It corresponds to a colouring of the generated graph Ɣ(G) obtained from G by replacing every edge by a clique. We estimate the minimum number of edges possible in a k
Results 1  10
of
1,203