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- Jin Akiyama, Mikio Kano
- Journal of Graph Theory
- 1985

- Mikio Kano, Saieed Akbari, Maryam Ghanbari, Mohammad Javad Nikmehr
- Electr. J. Comb.
- 1992

Let G be a graph. The core of G, denoted by G ∆ , is the subgraph of G induced by the vertices of degree ∆(G), where ∆(G) denotes the maximum degree of G. A k-edge coloring of G is a function f : E(G) → L such that |L| = k and f (e 1) = f (e 2) for all two adjacent edges e 1 and e 2 of G. The chromatic index of G, denoted by χ (G), is the minimum number k… (More)

- Atsushi Kaneko, M. Kano
- 2003

In this paper, we give a short survey on discrete geometry on red and blue points in the plane, most of whose results were obtained in the past decade. We consider balanced subdivision problems, geometric graph problems, graph embedding problems, Gallai-type problems and others. In this paper, we give a short survey on discrete geometry on red and blue… (More)

- Atsushi Kaneko, Mikio Kano, Kazuhiro Suzuki
- Journal of Graph Theory
- 2005

The tree partition number of an r-edge-colored graph G, denoted by t r (G), is the minimum number k such that whenever the edges of G are colored with r colors, the vertices of G can be covered by at most k vertex-disjoint monochromatic trees. We determine t 2 (K(n 1 , n 2 ,. .. , n k)) of the complete k-partite graph K(n 1 , n 2 ,. .. , n k). In… (More)

- Atsushi Amahashi, Mikio Kano
- Discrete Mathematics
- 1982

- Atsushi Kaneko, Mikio Kano, Kiyoshi Yoshimoto
- Int. J. Comput. Geometry Appl.
- 2000

We consider the following problem: For given two sets of red points and blue points in the plane respectively, we want to cover all these points with disjoint non-crossing alternating geometric paths of the same length. Determine the length of a path for which the above covering always exists under a trivial necessary condition on the numbers of red points… (More)

- Mikio Kano, Akio Sakamoto
- Networks
- 1983

- M. Kano, C. Merino, J. Urrutia
- 2003

Let P 1 , ..., P k be a collection of disjoint point sets in 2 in general position. We prove that for each 1 ≤ i ≤ k we can find a plane spanning tree T i of P i such that the edges of T 1 , ..., T k intersect at most (k − 1)(n − k) + (k)(k−1) 2 , where n is the number of points in P 1 ∪ ... ∪ P k. If the intersection of the convex hulls of P 1 , ..., P k… (More)

- Mikio Kano, Kazuhiro Suzuki, Miyuki Uno
- JCDCGG
- 2013

Let X be a set of multicolored points in the plane such that no three points are collinear and each color appears on at most ⌈|X|/2⌉ points. We show the existence of a non-crossing properly colored geometric perfect matching on X (if |X| is even), and the existence of a non-crossing properly colored geometric spanning tree with maximum degree at most 3 on… (More)