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Shortness parameters for planar graphs with faces of only one type

✍ Scribed by P. J. Owens

Publisher: John Wiley and Sons
Year: 1985
Tongue: English
Weight: 615 KB
Volume: 9
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190090310

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📜 SIMILAR VOLUMES

Regular planar graphs with faces of only

Regular planar graphs with faces of only two types and shortness parameters

✍ P. J. Owens 📂 Article 📅 1984 🏛 John Wiley and Sons 🌐 English ⚖ 931 KB

We construct a small non-Hamiltonian 3-connected trivalent planar graph whose faces are all 4-gons or 7-gons and show that the shortness coefficient of the class of such graphs is less than one. Then, by transforming non-Hamiltonian trivalent graphs into regular graphs of valency four or five, we ob

On shortness coefficients of simple 3-po

On shortness coefficients of simple 3-polytopal graphs with only one type of faces besides triangles

✍ Michal Tkáč 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 328 KB

We consider the class of simple 3-polytopes the faces of which are only triangles and 7-gons. We show that the shortness coefficient of this class is less than one. 6<q< 10.

Pentagonal 3-polytopal graphs with edges

Pentagonal 3-polytopal graphs with edges of only two types and shortness parameters

✍ Stanislav Jendrol'; Peter J. Owens 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 510 KB

We consider the class of pentagonal 3-polytopal graphs all of whose edges are incident either with two 3-valent vertices or with a 3-valent vertex and a q-valent vertex. For most values of q, (i) we find a small non-hamiltonian graph in the class and (ii) we show that the shortness exponent of the c

5-regular 3-polytopal graphs with edges

5-regular 3-polytopal graphs with edges of only two types and shortness exponents less than one

✍ J. Harant; P.J. Owens; M. Tkáč; H. Walther 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 309 KB

It is shown that, if q >/29 and q ~ 0 (mod 3), the infinite class of 5-regular 3-polytopal graphs whose edges are incident with either two triangles or a triangle and a q-gon contains nonhamiltonian members and even has shortness exponent less than one.

Shortness coefficients of simple 3-polyt

Shortness coefficients of simple 3-polytopal graphs with edges of only two types

✍ Michal Tkáč 📂 Article 📅 1992 🏛 Elsevier Science 🌐 English ⚖ 419 KB

TkSE, M., Shortness coefficients of simple 3-polytopal graphs with edges of only two types, Discrete Mathematics 103 (1992) 103-110. We consider two classes of simple 3-polytopal graphs whose edges are incident with either two S-gons or a 5-gon and q-gon (q = 26 or 27). We show that the shortness c

Simple 3-polytopal graphs with edges of

Simple 3-polytopal graphs with edges of only two types and shortness coefficients

✍ P.J Owens 📂 Article 📅 1986 🏛 Elsevier Science 🌐 English ⚖ 468 KB

We consider classes of simple 3-polytopal graphs whose edges are incident with either two 5-gons or a 5-gon and a q-gon (q > 5). We show that the shortness coefficient is less than one for all q 1> 28, settle a question raised by Jendrol and Tk~i~ in a recent paper in this journal and prove that all