Kenjiro Takazawa

Even factors, jump systems, and discrete convexity

A jump system, which is a set of integer lattice points with an exchange property, is an extended concept of a matroid. Some combinatorial structures such as the degree sequences of the matchings in an undirected graph are known to form a jump system. On the other hand, the maximum even factor problem is a generalization of the maximum matching problem into digraphs. When the given digraph has a certain property called odd-cycle-symmetry, this problem is polynomially solvable. The main result of this paper is that the degree sequences of all even factors in a digraph form a jump system if and only if the digraph is odd-cycle-symmetric. Furthermore, as a generalization, we show that the weighted even factors induce an M-convex (M-concave) function on a constant-parity jump system. These results suggest that even factors are a natural generalization of matchings and the assumption of odd-cycle-symmetry of digraphs is essential.

Finding 2-Factors Closer to TSP Tours in Cubic Graphs

In this paper we are interested in algorithms for finding

A Weighted kt, t-Free t-Factor Algorithm for Bipartite Graphs

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A weighted even factor algorithm

-factors that cover certain prescribed edge-cuts in bridgeless cubic graphs. Since a Hamilton cycle is a 2-factor covering all edge-cuts, imposing the constraint of covering those edge-cuts makes the obtained

A proof of Cunningham's conjecture on restricted subgraphs and jump systems

2

The Independent Even Factor Problem

-factor closer to a Hamilton cycle. We present an algorithm for finding a minimum-weight

Decomposition Theorems for Square-free 2-matchings in Bipartite Graphs

2

Randomized strategies for cardinality robustness in the knapsack problem

-factor covering all the

A 7/6-approximation algorithm for the minimum 2-edge connected subgraph problem in bipartite cubic graphs

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Posimodular Function Optimization

-edge cuts in weighted bridgeless cubic graphs, together with a polyhedral description of such 2-factors and that of perfect matchings intersecting all the 3-edge cuts in exactly one edge. We further give an algorithm for finding a 2-factor covering all the