منابع مشابه
Polarities and 2k-cycle-free graphs
Let C2k be the cycle on 2k vertices, and let ex(v, C2k) denote the greatest number of edges in a simple graph on v vertices which contains no subgraph isomorphic to C2k. In this paper we discuss a method which allows one to sometimes improve numerical constants in lower bounds for ex(v,C2k). The method utilizes polarities in certain rank two geometries. It is applied to refute some conjectures ...
متن کاملA result on 2k-cycle-free bipartite graphs
Let G be a bipartite graph with vertex parts of orders N and M , and X edges. I prove that if G has no cycles of length 2l, for all l ∈ [2, 2k], and N ≥ M , then X < M 1 2 N k+1 2k + O(N).
متن کاملProperties of Certain Families of 2k-Cycle-Free Graphs
Let v = v(G) and e = e(G) denote the order and size of a simple graph G, respectively. Let G = {Gi}i≥1 be a family of simple graphs of magnitude r > 1 and constant λ > 0, i.e. e(Gi) = (λ+ o(1))v(Gi), i→∞. For any such family G whose members are bipartite and of girth at least 2k + 2, and every integer t, 2 ≤ t ≤ k − 1, we construct a family G̃t of graphs of same magnitude r, of constant greater ...
متن کاملOn 2k-Twisted Graphs
We define the concept of a k-twisted chain in a (directed) graph and the concept of a 2k-twisted graph. We show that for a 2k-twisted graph the set of algebraic 2k-twisted cycles is an integral spanning set for the integral flow module of G. Since a graph is O-twisted if and only if it is strongly connected, our result generalizes the well-known theorem that there is a basis for the flow space ...
متن کاملCycle-maximal triangle-free graphs
We conjecture that the balanced complete bipartite graph K⌊n/2⌋,⌈n/2⌉ contains more cycles than any other n-vertex triangle-free graph, and we make some progress toward proving this. We give equivalent conditions for cycle-maximal triangle-free graphs; show bounds on the numbers of cycles in graphs depending on numbers of vertices and edges, girth, and homomorphisms to small fixed graphs; and u...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1999
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(99)90107-3