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Tight and Untight Triangulations of Surfaces by Complete Graphs

โœ Scribed by J.L. Arocha; J. Bracho; V. Neumannlara

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
570 KB
Volume
63
Category
Article
ISSN
0095-8956

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โœฆ Synopsis

Triangular embeddings of complete graphs into surfaces are studied through the notion of tightness which is a natural combinatorial generalization of connectedness for graphs. By means of a construction which "couples" two such surfaces to produce a new one, the existence of untight complete triangular embeddings is proved and the known archive of tight ones is broadened. In particular, (K_{3 \mid}) admits a tight and an untight triangular embedding into the same surface. Therefore, complete graphs may triangulate the same surface in nonisomorphic ways. ic 1995 Academic Press. Inc.

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