Consistent Estimate of Innovations Model**This work is supported by JSPS KAKENHI Grant Number 15K06146.

A degree sum condition on the order, the connectivity and the independence number for Hamiltonicity

In [Graphs Combin. 24 (2008) 469–483.], the third author and the fifth author conjectured that if G is a k-connected graph such that σk+1(G) ≥ |V (G)|+κ(G)+(k−2)(α(G)−1), then G contains a Hamiltonian cycle, where σk+1(G), κ(G) and α(G) are the minimum degree sum of k + 1 independent ∗Supported by JSPS KAKENHI Grant Number 26800083. †Supported by JSPS KAKENHI Grant Number 26800086. ‡Supported b...

A Relationship Between Thomassen's Conjecture and Bondy's Conjecture

In 1986, Thomassen posed the following conjecture: every 4-connected line graph has a Hamiltonian cycle. As a possible approach to the conjecture, many researchers have considered statements that are equivalent or related to it. One ∗Email address: [email protected] Research partly supported by project P202/12/G061 of the Czech Science Foundation and by the European Regional Development Fund (ER...

Supported by an unrestricted educational grant.

Stochastic Packing Integer Programs with Few Queries

We consider a stochastic variant of the integer linear programming problem, which contains random variables in the objective vector. We are allowed to reveal each entry of the objective vector by conducting a query, and the task is to find a good solution by conducting a small number of queries. We propose adaptive and nonadaptive algorithms for this problem, and provide a general technique for...

Linear-Time FPT Algorithms via Half-Integral Non-returning A-path Packing

A recent trend in the design of FPT algorithms is exploiting the half-integrality of LP relaxations. In other words, starting with a half-integral optimal solution to an LP relaxation, we assign integral values to variables one-by-one by branch and bound. This technique is general and the resulting time complexity has a low dependency on the parameter. However, the time complexity often becomes...