The secret santa problem.

Liberti, Leo and Raimondi, Franco ORCID: https://orcid.org/0000-0002-9508-7713 (2008) The secret santa problem. Lecture Notes in Computer Science, 5034 . pp. 271-279. ISSN 0302-9743 [Article] (doi:10.1007/978-3-540-68880-8_26)

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Abstract

Consider a digraph where the vertices represent people and
an arc (i, j) represents the possibility of i giving a gift to j. The basic question we pose is whether there is an anonymity-preserving “gift assignment” such that each person makes and receives exactly one gift, and such that no person i can infer the remaining gift assignments from the fact that i is assigned to give a gift to j. We formalize this problem as a graph property involving vertex disjoint circuit covers, give a polynomial algorithm to decide this property for any given graph and provide a computational validation of the algorithm.

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