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The Odd-Distance Plane Graph

✍ Scribed by Hayri Ardal; Ján Maňuch; Moshe Rosenfeld; Saharon Shelah; Ladislav Stacho

Book ID
106149963
Publisher
Springer
Year
2009
Tongue
English
Weight
315 KB
Volume
42
Category
Article
ISSN
0179-5376

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📜 SIMILAR VOLUMES

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✍ Hiroshi Maehara; Katsuhiro Ota; Norihide Tokushige 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 290 KB

We prove that every finite simple graph can be drawn in the plane so that any two vertices have an integral distance if and only if they are adjacent. The proof is constructive.

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✍ Severino V. Gervacio; Hiroshi Maehara 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 150 KB

The subdivision number of a graph G is defined to be the minimum number of extra vertices inserted into the edges of G to make it isomorphic to a unit-distance graph in the plane. Let t (n) denote the maximum number of edges of a C 4 -free graph on n vertices. It is proved that the subdivision numbe