Combinatorial Geometry and Graph Theory: Indonesia-Japan by Jin Akiyama, Edy Tri Baskoro, Mikio Kano

By Jin Akiyama, Edy Tri Baskoro, Mikio Kano

This booklet constitutes the completely refereed post-proceedings of the Indonesia-Japan Joint convention on Combinatorial Geometry and Graph conception, IJCCGGT 2003, held in Bandung, Indonesia in September 2003.

The 23 revised papers offered have been conscientiously chosen in the course of rounds of reviewing and development. one of the themes coated are coverings, convex polygons, convex polyhedra, matchings, graph colourings, crossing numbers, subdivision numbers, combinatorial optimization, combinatorics, spanning timber, a variety of graph characteristica, convex our bodies, labelling, Ramsey quantity estimation, etc.

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Extra resources for Combinatorial Geometry and Graph Theory: Indonesia-Japan Joint Conference, IJCCGGT 2003, Bandung, Indonesia, September 13-16, 2003, Revised Selected Papers

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8. M. Kobayashi and G. Nakamura, Uniform coverings of 2-paths with 6-cycles in the complete graph, manuscript. jp Abstract. e. the n-gon is a net of the polyhedron. In this paper we identify all convex polyhedra which are foldable from an equilateral triangle. 1 Introduction In [3, 4] the study of folding polygons to convex polyhedra was studied. In [3] they discussed the systematic construction of all polyhedra foldable from a unit square. In this paper we follow this line of research by identifying all polyhedra which are foldable from an equilateral triangle.

The n-gon is a net of the polyhedron. In this paper we identify all convex polyhedra which are foldable from an equilateral triangle. 1 Introduction In [3, 4] the study of folding polygons to convex polyhedra was studied. In [3] they discussed the systematic construction of all polyhedra foldable from a unit square. In this paper we follow this line of research by identifying all polyhedra which are foldable from an equilateral triangle. In subsequent papers [1, 2], we identify all polyhedra which are foldable from regular n-gons (n ≥ 5).

C Springer-Verlag Berlin Heidelberg 2005 26 J. Akiyama, M. Kobayashi, and G. 1 There exists uniform coverings of 2-paths with 6-paths in Kn when n = 7, 10, 11, 12, 15, 16, 17. Proof. Let Vn = {0, 1, 2, . . , n − 1} be the vertex set of Kn . We call a uniform covering of 2-paths with Hamilton cycles in Kn a Dudeny set in Kn . It is known that there exists a Dudeny set in Kn when 3 ≤ n ≤ 20 [1]. We denote it by Dn . (1) n = 7 For a Hamilton cycle in D8 , H = (7, a1 , a2 , . . , a7 ), define a 6-path H ∗ : H ∗ = [a1 , a2 , .

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