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A perfect matching is a matching of all the vertices of a graph. In other words, a perfect matching is a set of edges such that each vertex of the graph is incident to exactly one edge in the set.
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The perfect matching problem of planar graph
We know that connectivity is closely related to the Hamiltonian of planar graphs.
The most famous result is the Tutte theorem.
Theorem (Tutte, 1956). A 4-connected planar graph has a Hamiltonian cycl …
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The perfect matching problem of planar graph
The following article provides a positive answer to my question. Yes, it is possible to prove that a 4-connected planar graph has a perfect matching or almost perfect matching even without using the H …