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- Robert E. L. Aldred, Jun Fujisawa, Akira Saito
- Journal of Graph Theory
- 2010

- Jun Fujisawa, Atsuhiro Nakamoto, Kenta Ozeki
- J. Comb. Theory, Ser. B
- 2013

Let G be a 3-connected bipartite graph with partite sets X ∪ Y which is em-beddable in the torus. We shall prove that G has a Hamiltonian cycle if (i) G is blanced , i.e., |X| = |Y |, and (ii) each vertex x ∈ X has degree four. In order to prove the result, we establish a result on orientations of quadrangular torus maps possibly with multiple edges. This… (More)

A weighted graph is one in which every edge e is assigned a nonnegative number, called the weight of e. The weight of a graph is defined as the sum of the weights of its edges. In 2-edge-colored complete graph, by using Ramsey-type theorems, we obtain the existence of monochromatic subgraph which have many edges compared with its order. In this paper, we… (More)

- Jun Fujisawa, Adriana Hansberg, +4 authors JUN FUJISAWA
- 2008

For a positive integer k, a set of vertices S in a graph G is said to be a k-dominating set if each vertex x in V (G) − S has at least k neighbors in S. The order of a smallest k-dominating set of G is called the k-domination number of G and is denoted by γ k (G). In Blidia, Chellali and Favaron [Australas. they proved that a tree T satisfies α(T) ≤ γ 2 (T)… (More)

- Jun Fujisawa, Liming Xiong, Kiyoshi Yoshimoto, Shenggui Zhang
- Journal of Graph Theory
- 2007

Let G be a simple graph with order n and minimum degree at least two. In this paper, we prove that if every odd branch-bond in G has an edge-branch, then its line graph has a 2-factor with at most 3n−2 8 components. For a simple graph with minimum degree at least three also, the same conclusion holds.

- Robert E. L. Aldred, Yoshimi Egawa, Jun Fujisawa, Katsuhiro Ota, Akira Saito
- Journal of Graph Theory
- 2011

Ota and Tokuda [2] gave a minimum degree condition for a K1,n-free graph to have a 2-factor. Though their condition is best-possible, their sharpness examples have edge-connectivity one. In this paper, we improve their minimum degree condition for K1,n-free graphs with large connectivity or large edge-connectivity. Our bound is sharp, and together with Ota… (More)

Given a graph G = (V, E) and a spanning subgraph H of G (the backbone of G), a backbone coloring for G and H is a proper vertex coloring V → {1, 2,. . .} of G in which the colors assigned to adjacent vertices in H differ by at least two. In a recent paper, backbone colorings were introduced and studied in cases were the backbone is either a spanning tree or… (More)

- Jun Fujisawa, Akira Saito
- Combinatorics, Probability & Computing
- 2012

In this paper, we consider pairs of forbidden subgraphs that imply the existence of a 2-factor in a graph. For d ≥ 2, let G d be the set of connected graphs of minimum degree at least d. Let F 1 and F 2 be connected graphs and let H be a set of connected graphs. Then {F 1 , F 2 } is said to be a forbidden pair for H if every {F 1 , F 2 }-free graph in H of… (More)

- Hikoe Enomoto, Jun Fujisawa, Katsuhiro Ota
- Ars Comb.
- 2001

A weighted graph is a graph in which each edge e is assigned a non-negative number w(e), called the weight of e. The weight of a cycle is the sum of the weights of its edges. The weighted degree d w (v) of a vertex v is the sum of the weights of the edges incident with v. In this paper, we prove the following result: Suppose G is a 2-connected weighted… (More)

- M Salman, H J Broersma, +21 authors H A N M J Salman
- 2005

No part of this work may be reproduced by print, photocopy or any other means without the permission in writing from the author. Preface In the name of Allaah, the Most Gracious and the Most Merciful. All the praises and thanks are to Allaah, the Lord of the 'aalamiin (mankind, jinn and all that exists). in three topics of graph theory, namely: spanning… (More)