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

By Jin Akiyama, Edy Tri Baskoro, Mikio Kano

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

The 23 revised papers offered 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 timber, a number of graph characteristica, convex our bodies, labelling, Ramsey quantity estimation, etc.

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

Example text

The three vertices of the triangle converge at a point. a. The point of convergence is glued to a point which does not lie on the perimeter of the triangle. b. The point of convergence is glued to a point which lies on the perimeter of the triangle. Case 2. Only two of the three vertices of the triangle converge at a point. a. The point of convergence is glued to a point which lies on the side connecting the two vertices. b. The point of convergence is glued to a point which lies on a side of the triangle having one of the vertices as an end point but not the other.

Let U, V be uniform coverings of 2-paths with 6-paths in Km , K10 , respectively. Then we have the following claim. 14 (1) When m is odd, U ∪ V ∪ (P ∪ Q) ∪ (T ∪ ρT ) is a uniform covering of 2-paths with 6-paths in Km+10 . (2) When m is even, U ∪ V ∪ (P ∪ Q) ∪ (W ∪ ρW) is a uniform covering of 2-paths with 6-paths in Km+10 . Proof. (1) The 2-paths in Km and the 2-paths in K10 are covered with U ∪ V exactly once. 7. They are covered exactly once since the 2-paths belonging to (P ∪Q)∪(T ∪ρT ) are distinct.

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. Combinatorial Theory (A) 62 (1993) 26-42. 5. M. Kobayashi and G. Nakamura, Uniform coverings of 2-paths by 4-paths, Australasian J.

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