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

By Jin Akiyama, Edy Tri Baskoro, Mikio Kano

This e-book 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 awarded have been rigorously chosen in the course of rounds of reviewing and development. one of the themes lined are coverings, convex polygons, convex polyhedra, matchings, graph colourings, crossing numbers, subdivision numbers, combinatorial optimization, combinatorics, spanning bushes, a variety of graph characteristica, convex our bodies, labelling, Ramsey quantity estimation, etc.

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Extra info 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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Therefore An holds for all n ≥ 7 and n ≡ 0, 1, 2 (mod 5). 1. Uniform Coverings of 2-Paths with 6-Paths in the Complete Graph 33 References 1. K. Heinrich, M. Kobayashi and G. Nakamura, Dudeney’s round table problem, Discrete Mathematics 92 (1991) 107-125. 2. K. Heinrich, D. Langdeau and H. Verrall, Covering 2-paths uniformly, J. Combin. Des. 8 (2000) 100-121. 3. K. Nonay, Exact coverings of 2-paths by 4-cycles, J. Combin. Theory (A) 45 (1987) 50-61. 4. M. Kobayashi, Kiyasu-Z. and G. Nakamura, A solution of Dudeney’s round table problem for an even number of people, J.

Case 1. The three vertices of the triangle converge at a point. Case 1a. 1(a). 1(b)). (a) (b) Fig. 1 Case 1b. The sum of the angles at the vertices is π and the angle formed by the side at the point is also π, so the total sum of the angles is 2π, hence this point of Foldings of Regular Polygons to Convex Polyhedra I: Equilateral Triangles 37 convergence cannot be one of vertices of a convex polyhedron. Consequently, this point must either lie on an edge of the resulting polyhedron or else be an interior point of one of the faces of the polyhedron.

It is trivial that π(W) ⊂ {[x, u, y], [u, x, y] | u = y }. Therefore we have the claim. a, b, c, d, e; x, y ∈ Vm , x = 32 J. Akiyama, M. Kobayashi, and G. Nakamura Define the vertex-permutation ρ in Km+10 same as before: ρ = (a f )(b g)(c h) (d i)(e j), then we have the following claim. The proof is trivial. 12 When m is even, π(ρW) = {[x, u, y], [u, x, y] | u = f, g, h, i, j; x, y ∈ y }. 13. 13 When m is even, π(W ∪ ρW) = Π3 ∪ Π4 . Proof. 12. (III) Final step. Let U, V be uniform coverings of 2-paths with 6-paths in Km , K10 , respectively.

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