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Large cycles in random generalized Johnson graphs

Institution:	1. Moscow Institute of Physics and Technology (National Research University), Department of Discrete Mathematics, Dolgoprudny, Moscow Region, Russian Federation;2. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow, Russian Federation;3. Adyghe State University, Caucasus Mathematical Center, Maykop, Republic of Adygea, Russian Federation;4. Institute of Mathematics and Computer Science, Buryat State University, Ulan-Ude, Buryat Republic, Russian Federation;5. The Russian Presidential Academy of National Economy and Public Administration, Moscow, Russian Federation;6. Moscow Center for Fundamental and Applied Mathematics, Moscow, Russian Federation

Abstract:	This paper studies thresholds in random generalized Johnson graphs for containing large cycles, i.e. cycles of variable length growing with the size of the graph. Thresholds are obtained for different growth rates.

Keywords:	Random graphs Johnson graph Kneser graph Large cycles Threshold
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