Abstract
AbstractIn [4] it was shown that in a 5‐connected even planar triangulation G, every matching M of size can be extended to a perfect matching of G, as long as the edges of M lie at distance at least 5 from each other. Somewhat later in [7], the following result was proved. Let be a 5‐connected triangulation of a surface different from the sphere. Let be the Euler characteristic of . Suppose with even and and are two matchings in such that . Further suppose that the pairwise distance between two elements of is at least 5 and the face‐width of the embedding of in is at least . Then there is a perfect matching in which contains such that . In the present paper, we present some results which, in a sense, lie in the gap between the two above theorems, in that they deal with restricted matching extension in a planar triangulation when a set of vertices which lie pairwise at sufficient distance from one another has been deleted. In particular, we prove a planar analogue of the result in [7] stated above.
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