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On Superconnectivity of (4, g)Cages with Even Girth
"... A (k, g)cage is a kregular graph with girth g that has the fewest number of vertices. It has been conjectured [Fu, Huang, and Rodger, Connectivity of cages, J. Graph Theory 24 (1997), 187191] that all (k, g)cages are kconnected for k ≥ 3. A connected graph G is said to be superconnected if ever ..."
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A (k, g)cage is a kregular graph with girth g that has the fewest number of vertices. It has been conjectured [Fu, Huang, and Rodger, Connectivity of cages, J. Graph Theory 24 (1997), 187191] that all (k, g)cages are kconnected for k ≥ 3. A connected graph G is said to be superconnected
Girth of Sparse Graphs
 2002), 194  200. ILWOO CHO
"... Recently, Bollobás, Janson and Riordan introduced a very general family of random graph models, producing inhomogeneous random graphs with Θ(n) edges. Roughly speaking, there is one model for each kernel, i.e., each symmetric measurable function from [0,1] 2 to the nonnegative reals, although the d ..."
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Cited by 79 (6 self)
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Recently, Bollobás, Janson and Riordan introduced a very general family of random graph models, producing inhomogeneous random graphs with Θ(n) edges. Roughly speaking, there is one model for each kernel, i.e., each symmetric measurable function from [0,1] 2 to the nonnegative reals, although
On the Girth of Digraphs
 Discrete Math
, 1998
"... It was conjectured by Caccetta and Haggkvist in 1978 that the girth of every digraph with n vertices and minimum outdegree r is at most dn=re. The conjecture was proved for r = 2 by Caccetta and Haggkvist, for r = 3 by Hamidoune and for r = 4; 5 by Ho'ang and Reed. In this paper, the followi ..."
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Cited by 11 (3 self)
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, the following two main results are proved: 1. The diameter of every strongly connected digraph of order n with girth g is at most n \Gamma g + t, where t is the number of vertices having outdegree exactly 1. As a consequence, a short, selfcontained proof of Caccetta and Haggkvist's result is obtained
Minors in Graphs of Large Girth
 J. Combin. Theory B
, 1988
"... We show that for every odd integer g 5 there exists a constant c such that every graph of minimum degree r and girth at least g contains a minor of minimum degree at least cr . This is best possible up to the value of the constant c for g = 5; 7 and 11. More generally, a wellknown conjecture ..."
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Cited by 5 (0 self)
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We show that for every odd integer g 5 there exists a constant c such that every graph of minimum degree r and girth at least g contains a minor of minimum degree at least cr . This is best possible up to the value of the constant c for g = 5; 7 and 11. More generally, a wellknown
On monomial graphs of girth eight
, 2005
"... Let e be a positive integer, p be an odd prime, q = pe,andFqbe the finite field of q elements. Let f2,f3 ∈ Fq[x,y]. The graph G = Gq(f2,f3) is a bipartite graph with vertex partitions P = F3 q and L = F3q,and edges defined as follows: a vertex (p) = (p1,p2,p3) ∈ P is adjacent to a vertex [l] =[l1, ..."
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Let e be a positive integer, p be an odd prime, q = pe,andFqbe the finite field of q elements. Let f2,f3 ∈ Fq[x,y]. The graph G = Gq(f2,f3) is a bipartite graph with vertex partitions P = F3 q and L = F3q,and edges defined as follows: a vertex (p) = (p1,p2,p3) ∈ P is adjacent to a vertex [l] =[l1
GIRTH AND CHROMATIC NUMBER OF GRAPHS
"... Abstract. This paper will look at the relationship between high girth and high chromatic number in both its finite and transfinite incarnations. On the one hand, we will demonstrate that it is possible to construct graphs with high oddgirth and high chromatic number in all cases. We will then look a ..."
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at a theorem which tells us why, at least in the transfinite case, it is impossible to generalize this to include even cycles. Finally, we will use the probabilistic method to show why it is possible to construct graphs of any given finite girth
LARGEGIRTH ROOTS OF GRAPHS
, 2010
"... We study the problem of recognizing graph powers and computing roots of graphs. We provide a polynomial time recognition algorithm for rth powers of graphs of girth at least 2r + 3, thus improving a bound conjectured by Farzad et al. (STACS 2009). Our algorithm also finds all rth roots of a give ..."
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Cited by 1 (0 self)
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We study the problem of recognizing graph powers and computing roots of graphs. We provide a polynomial time recognition algorithm for rth powers of graphs of girth at least 2r + 3, thus improving a bound conjectured by Farzad et al. (STACS 2009). Our algorithm also finds all rth roots of a
Ramanujan Graphs With Small Girth
"... We construct an infinite family of (q +1) regular Ramanujan graphs X n of girth 1. We also give covering maps X n+1 ! X n such that the minimal common covering of all the X n 's is the universal covering tree. ..."
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Cited by 3 (2 self)
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We construct an infinite family of (q +1) regular Ramanujan graphs X n of girth 1. We also give covering maps X n+1 ! X n such that the minimal common covering of all the X n 's is the universal covering tree.
REGULAR GRAPHS OF GIVEN GIRTH
, 2007
"... This paper gives an introduction to the area of graph theory dealing with properties of regular graphs of given girth. A large portion of the paper is based on exercises and questions proposed by László Babai in his lectures and in his Discrete ..."
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This paper gives an introduction to the area of graph theory dealing with properties of regular graphs of given girth. A large portion of the paper is based on exercises and questions proposed by László Babai in his lectures and in his Discrete
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
Results 1  10
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5,607