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On the connectivity of maximal planar graphs
Author(s) -
Hakimi S. L.,
Schmeichel E. F.
Publication year - 1978
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190020404
Subject(s) - combinatorics , mathematics , planar graph , vertex (graph theory) , planar , graph , vertex connectivity , discrete mathematics , computer science , computer graphics (images)
Let d 1 ⩾ d 2 ⩾ … ⩾ d p be the vertex degrees of a maximal planar graph G . Etourneau has shown that if d 1 ⩽ 6 and d p = 5, then G is 5‐connected. We generalize Etourneau's result by giving sufficient conditions in terms of the vertex degrees for G to be d p ‐connected.