On a class of degenerate extremal graph problems

@article{Faudree1983OnAC,
  title={On a class of degenerate extremal graph problems},
  author={R. Faudree and M. Simonovits},
  journal={Combinatorica},
  year={1983},
  volume={3},
  pages={83-93}
}
Given a class ℒ of (so called “forbidden”) graphs, ex (n, ℒ) denotes the maximum number of edges a graphGn of ordern can have without containing subgraphs from ℒ. If ℒ contains bipartite graphs, then ex (n, ℒ)=O(n2−c) for somec>0, and the above problem is calleddegenerate. One important degenerate extremal problem is the case whenC2k, a cycle of 2k vertices, is forbidden. According to a theorem of P. Erdős, generalized by A. J. Bondy and M. Simonovits [32, ex (n, {C2k})=O(n1+1/k). In this paper… Expand
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References

SHOWING 1-10 OF 12 REFERENCES
Cycles of even length in graphs
  • 336
  • PDF
ON A PROBLEM OF GRAPH THEORY
  • 524
  • PDF
On Minimal graphs of maximum even girth
  • 106
On paul turán's influence on graph theory
  • 7
On graphs that do not contain a Thomsen graph
  • 341
  • Highly Influential
  • PDF
The evolution of random graphs
  • 5,475
  • PDF
Graph theory
  • 305
On an extremal problem in graph theory
  • 862
  • PDF
...
1
2
...