Random lifts of $K_5\setminus e$ are 3-colourable

Amit, Linial, and Matou\vsek (Random lifts of graphs III: independence and chromatic number, Random Struct. Algorithms, 2001) have raised the following question: Is the chromatic number of random $h$-lifts of $K_5$ asymptotically (for $h\to\infty$) almost surely equal to a single number? In this paper, we offer the following partial result: The chromatic number of a random lift of $K_5\setminus e$ is asymptotically almost surely three.

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