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A local property of polyhedral maps on compact two-dimensional manifolds

✍ Scribed by S. Jendrol’; H.-J. Voss


Book ID
108316434
Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
97 KB
Volume
212
Category
Article
ISSN
0012-365X

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Subgraphs with Restricted Degrees of the
✍ S. Jendrol’; H.-J. Voss 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 276 KB

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