منابع مشابه
Biregular Cages of Girth Five
Let 2 6 r < m and g be positive integers. An ({r,m}; g)–graph (or biregular graph) is a graph with degree set {r,m} and girth g, and an ({r,m}; g)–cage (or biregular cage) is an ({r,m}; g)–graph of minimum order n({r,m}; g). If m = r+1, an ({r,m}; g)–cage is said to be a semiregular cage. In this paper we generalize the reduction and graph amalgam operations from [M. Abreu, G. Araujo–Pardo, C. ...
متن کاملOn the connectivity of cages with girth five, six and eight
A (δ, g)-cage is a regular graph of degree δ and girth g with the least possible number of vertices. Recently, some authors have addressed the problem of studying their connectivity parameters. In this direction, it was conjectured by Fu, Huang and Rodger that every (δ, g)-cage is maximally connected, i.e., it is δ-connected, and they proved this statement for δ = 3. We provide a new contributi...
متن کاملOn Hypergraphs of Girth Five
In this paper, we study r-uniform hypergraphs H 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 H has n vertices and a maximum number of edges, then |H| = 1 6 n + o(n). This also asymptotically determines the generalized Turán number T3(n, 8, 4). Some results are based on our bounds for the maximum s...
متن کاملOn superconnectivity of (4, g)-cages with even girth
A (k, g)-cage is a k-regular 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), 187-191] that all (k, g)-cages are k-connected for k ≥ 3. A connected graph G is said to be superconnected if every minimum cut-set S is the neighborhood of a vertex of minimum degree. Moreover, if G − S has pre...
متن کاملImproved Lower Bounds for the Orders of Even Girth Cages
The well-known Moore bound M(k, g) serves as a universal lower bound for the order of k-regular graphs of girth g. The excess e of a k-regular graph G of girth g and order n is the difference between its order n and the corresponding Moore bound, e = n −M(k, g). We find infinite families of parameters (k, g), g > 6 and even, for which we show that the excess of any k-regular graph of girth g is...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2013
ISSN: 1077-8926
DOI: 10.37236/2594