Download Computational Geometry and Graphs: Thailand-Japan Joint by Jin Akiyama, Mikio Kano, Toshinori Sakai PDF

By Jin Akiyama, Mikio Kano, Toshinori Sakai

This e-book constitutes the refereed court cases of the Thailand-Japan Joint convention on Computational Geometry and Graphs, TJJCCGG 2012, held in Bangkok, Thailand, in December 2012.
The 15 unique learn papers provided have been chosen from between six plenary talks, one detailed public speak and forty-one talks via individuals from approximately 20 international locations world wide. TJJCCGG 2012 supplied a discussion board for researchers operating in computational geometry, graph theory/algorithms and their applications.

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Additional resources for Computational Geometry and Graphs: Thailand-Japan Joint Conference, TJJCCGG 2012, Bangkok, Thailand, December 6-8, 2012, Revised Selected Papers

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218–227. ch Abstract. A set P of points in R2 is n-universal, if every planar graph on n vertices admits a plane straight-line embedding on P . Answering a question by Kobourov, we show that there is no n-universal point set of size n, for any n ≥ 15. Conversely, we use a computer program to show that there exist universal point sets for all n ≤ 10 and to enumerate all corresponding order types. Finally, we describe a collection G of 7 393 planar graphs on 35 vertices that do not admit a simultaneous geometric embedding without mapping, that is, no set of 35 points in the plane supports a plane straight-line embedding of all graphs in G.

It follows that there are at least 76 /12 > 9 804 pairwise nonisomorphic graphs in G. We now give an upper bound on the number of graphs of G that can be simultaneously embedded on a common point set. Lemma 9. At most 7 392 pairwise nonisomorphic graphs of G admit a simultaneous (plane straight-line) embedding without mapping. Proof. Consider a subset G ⊆ G of pairwise nonisomorphic graphs and a point set P that admits a simultaneous embedding of G . Since G is a class of maximal On Universal Point Sets for Planar Graphs 39 planar graphs, the convex hull of P must be a triangle.

10. Table 1. The number of (non-equivalent) n-universal point sets of size n n: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 ≥ 15 0 # universal point sets: 1 1 1 1 1 5 45 364 5 955 2 072 ? ? (170, 194) (5, 240) (69, 255) (63, 182) (253, 136) (194, 131) (149, 116) (101, 83) (138, 72) (255, 69) (0, 0) (92, 132) (180, 140) (148, 122) (36, 112) (177, 107) (219, 61) (65, 15) (126, 232) (28014, 34715) (150, 186) (151, 161) (124, 125) (162, 107) (254, 82) (29367, 32804) (25174, 31591) (29312, 31921) (29060, 31627) (61273, 56838) (21851, 49497) (23183, 47690) (4263, 46244) (26104, 43895) (26329, 42168) (45873, 38514) (43249, 34704) (27011, 31063) (29348, 30469) (28635, 30173) (36513, 24768) (88, 60) (2, 24) (32686, 28235) (30430, 8698) Fig.

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