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Star Decompositions of a Cyclic Polygon
Tomoki Nakamigawa
Let be a set of vertices on a circumference in the plane. Let be a set of directed line segments linking two vertices of . If forms a set of closed cycles and for al…
Structural Origins of Cubic Complexity in Pebble Motion
Tomoki Nakamigawa, Tadashi Sakuma
The pebble motion problem (PMP) asks whether one configuration of labeled pebbles on a graph can be transformed into another by moving pebbles to adjacent unoccupied vertices. It i…
A Correspondence between Chord Diagrams and Families of 0-1 Young Diagrams
Tomoki Nakamigawa
A chord diagram is a set of chords in which no pair of chords has a common endvertex. For a chord diagram having a crossing , by the chord expansion of wi…
On the average hitting times of the squares of cycles
Yoshiaki Doi, Norio Konno, Tomoki Nakamigawa +6
The exact formula for the average hitting time (HT, as an abbreviation) of simple random walks from one vertex to any other vertex on the square of an -vertex cycle grap…
Agent Arrangement Problem
Tomoki Nakamigawa, Tadashi Sakuma
An {\em arrangement} of an ordered pair of graphs is defined as a function from to such that, for each vertex of , the vertex-set $f^{-1…