## Abstract

For a graph G, a random n-lift of G has the vertex set V(G) × [n] and for each edge [u,v] ∈ E(G), there is a random matching between {u} × [n] and {v} × [n]. We present bounds on the chromatic number and on the independence number of typical random lifts, with G fixed and n → ∞ For the independence number, upper and lower bounds are obtained as solutions to certain optimization problems on the base graph. For a base graph G with chromatic number χ and fractional chromatic number χ _{f}, we show that the chromatic number of typical lifts is bounded from below by const ̇ √ χ/log χ and also by const ̇ χ/_{f}/log^{2} χ_{f} (trivially, it is bounded by x from above). We have examples of graphs where the chromatic number of the lift equals x almost surely, and others where it is a.s. O(χ/log χ). Many interesting problems remain open.

Original language | American English |
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Pages (from-to) | 1-22 |

Number of pages | 22 |

Journal | Random Structures and Algorithms |

Volume | 20 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2002 |