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Light Paths in Large Polyhedral Maps with Prescribed Minimum Degree

✍ Scribed by S. Jendrol; H.-J. Voss

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 961 KB
Volume: 11
Category: Article
ISSN: 1571-0653
DOI: 10.1016/s1571-0653(04)00083-6

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Subgraphs with Restricted Degrees of their Vertices in Large Polyhedral Maps on Compact Two-manifolds

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Let k ≥ 2, be an integer and M be a closed two-manifold with Euler characteristic χ(M) ≤ 0. We prove that each polyhedral map G on M, which has at least (8k 2 + 6k -6)|χ (M)| vertices, contains a connected subgraph H of order k such that every vertex of this subgraph has, in G, the degree at most 4k