Gaku Liu

activity

20102026

most citedSemistable reduction in characteristic 0

14 citations · 56 across the 17 of their papers we have counts for

collaborators

Showing 2012Show all

2 papers · 1 filter

math.CO2012★ 6 cited

Structure theorem for U5-free tournaments

Gaku Liu

Let $U_{5}$ be the tournament with vertices $v_{1}$ , ..., $v_{5}$ such that $v_{2} \to v_{1}$ , and $v_{i} \to v_{j}$ if $j - i \equiv 1$ , $2 (mod 5)$ and $i, j \neq = 1, 2$ . In th…

math.CO2012★ 2 cited

Various Theorems on Tournaments

Gaku Liu

In this thesis we prove a variety of theorems on tournaments. A \emph{prime} tournament is a tournament $G$ such that there is no $X \subseteq V (G)$ , $1 < ∣ X ∣ < ∣ V (G) ∣$ , such that…