Extremal Oriented Graphs and Erdős-hajnal Conjecture
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چکیده
For a (finite or infinite) family L of oriented graphs, a new parameter called the compressibility number of L and denoted by z(L) is defined. The main motivation is the application of this parameter in a special case of Turán-type extremal problems for digraphs, in which it plays the role of chromatic number in the classic extremal problems. We estimate this parameter for some special group of oriented graphs. Determining this parameter, in the most explicit possible form, for oriented graphs with bounded oriented coloring number (planar graph in particular) leads us to the famous Erdős-Hajnal conjecture.
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تاریخ انتشار 2009