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Perfect matching
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== Connection to Graph Coloring == An [[Edge coloring|edge-colored graph]] can induce a number of (not necessarily proper) [[Graph coloring|vertex colorings]] equal to the number of perfect matchings, as every vertex is covered exactly once in each matching. This property has been investigated in [[quantum physics]]<ref>Mario Krenn, Xuemei Gu, [[Anton Zeilinger]], [https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.119.240403 Quantum Experiments and Graphs: Multiparty States as Coherent Superpositions of Perfect Matchings], Phys. Rev. Lett. 119, 240403 β Published 15 December 2017</ref> and [[computational complexity theory]].<ref>[[Moshe Y. Vardi]], Zhiwei Zhang, [https://arxiv.org/abs/2301.09833 Solving Quantum-Inspired Perfect Matching Problems via Tutte's Theorem-Based Hybrid Boolean Constraints], arXiv:2301.09833 [cs.AI], [[International Joint Conference on Artificial Intelligence|IJCAI'23]]</ref>
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