Hajime Matsumura

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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)
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)