Turán′s Extremal Problem in Random Graphs: Forbidding Even Cycles

An Extremal Problem For Random Graphs And The Number Of Graphs With Large Even-Girth

We study the maximal number of edges a C2k-free subgraph of a random graph Gn;p may have, obtaining best possible results for a range of p = p(n). Our estimates strengthen previous bounds of F uredi 12] and Haxell, Kohayakawa, and Luczak 13]. Two main tools are used here: the rst one is an upper bound for the number of graphs with large even-girth, i.e., graphs without short even cycles, with a...

Even cycles in graphs

Even Cycles in Directed Graphs

It is proved that every strongly connected directed graph with n nodes and at least ⌊(n + 1)/4⌋ edges must contain an even cycle. This is best possible, and the structure of extremal graphs is discussed.

An ' S Extremal Problem in Randomgraphs : Forbidding Odd

Extremal graphs without 4-cycles

We prove an upper bound for the number of edges a C4-free graph on q 2 + q vertices can contain for q even. This upper bound is achieved whenever there is an orthogonal polarity graph of a plane of even order q. Let n be a positive integer and G a graph. We define ex(n,G) to be the largest number of edges possible in a graph on n vertices that does not contain G as a subgraph; we call a graph o...