Author
Jin Akiyama
Other affiliations: Tokai University
Bio: Jin Akiyama is an academic researcher from Tokyo University of Science. The author has contributed to research in topics: Polyhedron & Regular polygon. The author has an hindex of 17, co-authored 114 publications receiving 1148 citations. Previous affiliations of Jin Akiyama include Tokai University.
Topics: Polyhedron, Regular polygon, Polygon, Convex polytope, Polytope
Papers published on a yearly basis
Papers
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TL;DR: A degree factor of a graph is either an r-factor (regular of degree r) or an [m, n]-factor (with each degree between m and n) and in a component factor, each component is a prescribed graph.
Abstract: A degree factor of a graph is either an r-factor (regular of degree r) or an [m, n]-factor (with each degree between m and n). In a component factor, each component is a prescribed graph. Both kinds of factors are surveyed, and also corresponding factorizations.
125 citations
Journal Article•
TL;DR: In this paper, it is shown that for complete graphs, complete bipartite graphs, and their line graphs, it is possible to determine packing and covering invariants for graphs which involve paths and cycles.
Abstract: It is possible to define many variations of packing and covering invariants for graphs which involve paths and cycles. These can be given terminology which is sufficiently intuitive that one can remember the definitions, e.g., arboricity, linear arboricity, point arboricity, point linear arboricity, anarboricity, path number, unpath number, point anarboricity, and cyclicity. Most of these concepts are fundamental but it is not easy to determine the value of these invariants for general graphs. We investigate these concepts and relations among them for specific families of graphs. In particular, we determine them for complete graphs, complete bipartite graphs, and their line graphs.
124 citations
TL;DR: The condition under which there exists a simple alternating path P of A is determined, for the case when the 2 n points are the vertices of a convex polygon, and an O( n 2 ) algorithm to find such an alternating path (if it exists) is obtained.
48 citations
TL;DR: This work investigates the number D(F) defined as the largest d(G) such that G is a signed graph based on F and proves that 1 2 m− nm ≤D(F), which is the complete bipartite graph with t vertices in each part, for every graph F with n vertices and m edges.
47 citations
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2,670 citations
1,000 citations
01 Jan 1999
TL;DR: This is a survey of results on properties of random regular graphs, together with an exposition of some of the main methods of obtaining these results.
Abstract: This is a survey of results on properties of random regular graphs, together with an exposition of some of the main methods of obtaining these results. Related results on asymptotic enumeration are also presented, as well as various generalisations to random graphs with given degree sequence. A major feature in this area is the small subgraph conditioning method. When applicable, this establishes a relationship between random regular graphs with uniform distribution, and non-uniform models of random regular graphs in which the probability of a graph G is weighted according to the number of subgraphs G has of a certain type. Information can be obtained in this way on the probability of existence of various types of spanning subgraphs, such as Hamilton cycles and decompositions into perfect matchings. Uniformly distributed labelled random regular graphs receive most of the attention, but also included are several non-uniform models which come about in a natural way. Some of these appear as spin-offs from the small subgraph conditioning method, and some arise from algorithms which use simple approaches to generating random regular graphs. A quite separate role played by algorithms is in the derivation of random graph properties by analysing the performance of an appropriate greedy algorithm on a random regular graph. Many open problems and conjectures are given.
692 citations