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By Jin Akiyama, Midori Kobayashi, Gisaku Nakamura (auth.), Hiro Ito, Mikio Kano, Naoki Katoh, Yushi Uno (eds.)

This ebook constitutes the completely refereed post-conference court cases of the Kyoto convention on Computational Geometry and Graph concept, KyotoCGGT 2007, held in Kyoto, Japan, in June 2007, in honor of Jin Akiyama and Vašek Chvátal, at the party in their sixtieth birthdays.

The 19 revised complete papers, offered including five invited papers, have been conscientiously chosen in the course of rounds of reviewing and development from greater than 60 talks on the convention. All features of Computational Geometry and Graph idea are lined, together with tilings, polygons, very unlikely gadgets, coloring of graphs, Hamilton cycles, and components of graphs.

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Additional info for Computational Geometry and Graph Theory: International Conference, KyotoCGGT 2007, Kyoto, Japan, June 11-15, 2007. Revised Selected Papers

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Akiyama and C. Nara y X Y C B x D A Fig. 6. T ∪ To holds and the family {T ∪ To + (2k, 2l) : k, l ∈ ZZ} is a tiling, the family {S ∪ So + (2k, 2l)(e1 ,e2 ) : k, l ∈ ZZ} is also a tiling. By Proposition 4, S = T ∪ To is a development of a doubly covered square whose faces are congruent to the square ABCD, where A(0, −1), B(1, 0), C(0, 1), D(−1, 0). We call a tile T in the plane a k-omino if T consists of k congruent squares and if the intersection of any two of those squares is a point, one edge or empty.

The problem, both in its general Daescu’s research is supported by NSF grant CCF-0635013. 503. H. Ito et al. ): KyotoCGGT 2007, LNCS 4535, pp. 41–55, 2008. c Springer-Verlag Berlin Heidelberg 2008 42 O. Daescu and J. Luo P x1 t t −−→ SPst x2 X s s Fig. 1. A simple s-to-t path that turns on points in X (bold line), a shortest s-to-t path that turns on points in X and is not a simple path (dotted line), and the shortest s-to-t path in P (bold dashed line) form and in the special form studied in this paper, has been introduced in [3].

2 (b). Then r(G, H) = r(G , H) + 1. One of the walks of C contains (b, d). We replace (b, d) with bacd to obtain the set of alternating walks for F (G, H). Thus p(G, H) ≥ p(G , H). The bound (1) follows. Suppose that the colors of (a, c) and (b, d) are white, see Fig. 2 (c). Then r(G, H) = r(G , H). If the red edges (a, c) and (b, d) belong to different walks C1 and C2 of C , then C1 − {(a, c)} and C2 − {(b, d)} can be combined in one alternating walk with (a, b) and (c, d) in F (G, H), see Fig.

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