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- Shinya Fujita, Gary MacGillivray, Tadashi Sakuma
- Discrete Applied Mathematics
- 2016

A non-empty subset S of the vertices of a connected graph G = ( V ( G ) , E ( G ) ) is a safe set if, for every connected component C of G S and every connected component D of G - S , we have | C | ź… (More)

A triangulation is said to be even if each vertex has even degree. For even triangulations, define the N-flip and the P2-flip as two deformations preserving the number of vertices. We shall prove… (More)

- Raquel Águeda, Nathann Cohen, +9 authors Renyu Xu
- COCOA
- 2016

A safe set of a graph \(G=(V,E)\) is a non-empty subset S of V such that for every component A of G[S] and every component B of \(G[V \setminus S]\), we have \(|A| \ge |B|\) whenever there exists an… (More)

- Shinya Fujita, Tomoki Nakamigawa, Tadashi Sakuma
- Discrete Applied Mathematics
- 2015

Let G and H be graphs with the same number of vertices. We introduce a graph puzzle ( G , H ) in which G is a board graph and the set of vertices of H is the set of pebbles. A configuration of H on G… (More)

- Shuya Chiba, Shinya Fujita, Ken-ichi Kawarabayashi, Tadashi Sakuma
- Adv. Appl. Math.
- 2014

We prove a variant of a theorem of Corradi and Hajnal (1963) [4] which says that if a graph G has at least 3k vertices and its minimum degree is at least 2k, then G contains k vertex-disjoint cycles.… (More)

- Yusuke Higuchi, Atsuhiro Nakamoto, Katsuhiro Ota, Tadashi Sakuma
- Discrete Mathematics
- 2011

In this paper, we show that any two even triangulations on the torus with the same and sufficiently large number of vertices can be transformed into each other by a sequence of two specifically… (More)

- Kenji Kashiwabara, Tadashi Sakuma
- Discrete Mathematics
- 2006

We will show that Grinstead's Conjecture holds true ifmin(@a(G),@w(G))=<8. In other words; a circular partitionable graph G satisfyingmin(@a(G),@w(G))=<8is always a so-called ''CGPW-graph''.

- Komei Fukuda, Alain Prodon, Tadashi Sakuma
- Theor. Comput. Sci.
- 2001

In this paper we study two lemmas on acyclic orientations and totally cyclic orientations of a graph, which can be derived from the shelling lemma in vector subspaces. We give simple graph… (More)

- Ravindra B. Bapat, Shinya Fujita, +4 authors Zsolt Tuza
- Networks
- 2018

Let G = (V, E) be a graph and let w : V → ℝ>0 be a positive weight function on the vertices of G. For every subset X of V, let w(X) ≔ ∑v∈Gw(v). A non-empty subset ∑ is a weighted safe set if, for… (More)

- Tadashi Sakuma
- Journal of Graph Theory
- 1997