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In this paper, we give a sufficient condition for a graph to have a degree bounded spanning tree. Let n ≥ 1, k ≥ 3, c ≥ 0 and G be an n-connected graph. Suppose that for every independent set S ⊆ V(G) of cardinality n(k − 1) + c + 2, there exists a vertex set X ⊆ S of cardinality k such that the degree sum of vertices in X is at least |V(G)| − c − 1. Then G… (More)

We propose a method for improving motivation to participate in sensing services by presenting rankings in multidimensional hierarchical sets. We call this method <i>Top of Worlds</i>. Because previously proposed methods only rank a user among all other users, many have little chance of being ranked in the top group, resulting in little motivation to… (More)

- Hideo Aoki, Masato Ando, Hajime Matsumura
- 1996

Hofstadter's diagram, or the energy spectrum against the magnetic field in tight-binding systems, is obtained for the models having flat (dispersionless) one-electron band(s) that have originally been proposed for itinerant spin ferromagnetism. Magnetic fields preserve those flat bands that arise from a topological reason, while dispersions emerge in a… (More)

A k-tree is a tree with maximum degree at most k. In this paper, we give a degree sum condition for a graph to have a spanning k-tree in which specified vertices have degree less than k. We denote by σ k (G) the minimum value of the degree sum of k independent vertices in a graph G. Let k ≥ 3 and s ≥ 0 be integers, and suppose G is a connected graph and σ k… (More)

- Hajime Matsumura, References, M N Ellingham, Y Nam, H.-J Voss
- 2015

A k-tree is a tree with maximum degree at most k. In this paper, we give a degree sum condition for a graph to have a spanning k-tree in which specified vertices have degree less than k. We denote by σ k (G) the minimum value of the degree sum of k independent vertices in a graph G. Let k ≥ 3 and s ≥ 0 be integers, and suppose G is a connected graph and σ k… (More)

Although conjunctival squamous cell carcinoma is known to develop as a result of chronic irritation from wearing an ocular prosthesis, orbital sebaceous gland carcinoma arising in an anophthalmic pocket is extremely rare. We report a 68-year-old female who developed a sebaceous gland carcinoma 65 years after her right eye was enucleated (at the age of three… (More)