论文信息 - 5-regular 3-polytopal Graphs with Edges of Only Two Types and Shortness Exponents Less than One

5-regular 3-polytopal Graphs with Edges of Only Two Types and Shortness Exponents Less than One

Abstract 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.

[1] Stanislav Jendrol',et al. Convex 3-polytopes with exactly two types of edges , 1990, Discret. Math..

[2] W. T. Tutte. On Hamiltonian Circuits , 1946 .

[3] Stanislav Jendroľ,et al. Longest circuits in triangular and quadrangular $3$-polytopes with two types of edges , 1990 .

[4] P. J. Owens,et al. Shortness parameters of families of regular planar graphs with two or three types of face , 1982, Discret. Math..

[5] Hansjoachim Walther,et al. Über das Problem der Existenz von HAMILTONkreisen in planaren, regulären Graphen† , 1969 .

[6] Hansjoachim Walther,et al. Shortness Exponents of Families of Graphs , 1973, J. Comb. Theory, Ser. A.

[7] Peter J. Owens. Regular planar graphs with faces of only two types and shortness parameters , 1984, J. Graph Theory.

[8] Stanislav Jendrol',et al. Pentagonal 3-polytopal graphs with edges of only two types and shortness parameters , 1995, Discret. Math..