# Jun Fujisawa

In this chapter we present some notations and give a survey of the existing results about three topics of graph theory that are considered in this thesis, namely: spanning 2-connected subgraphs of grid graphs, Ramsey numbers for paths versus other graphs, and a general framework for coloring problems. 1.1 Notation and terminology Throughout this thesis, we(More)
• J. Comb. Theory, Ser. B
• 2013
Let G be a 3-connected bipartite graph with partite sets X ∪ Y which is embeddable 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)
• Journal of Graph Theory
• 2010
For a connected graph H, a graph G is said to be H-free if G does not contain an induced subgraph which is isomorphic to H, and for a set of connected graphs H, G is said to be H-free if G is H-free for every H ∈ H. The set H is called a forbidden subgraph. In particular, if |H| = 2 (resp. |H| = 3), we often call H a forbidden pair (resp. forbidden triple).(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(More)
A graph is called a weighted graph when each edge e is assigned a nonnegative number w(e), called the weight of e. For a vertex v of a weighted graph, d(v) is the sum of the weights of the edges incident with v. For a subgraph H of a weighted graph G, the weight of H is the sum of the weights of the edges belonging to H . In this paper, we give a new(More)
• Pathology international
• 1998
Histiocytoid breast carcinoma (HBC) is a rare variant of breast carcinoma and often causes a diagnostic dilemma because of its histological similarities to some types of breast cancer and benign lesions. To elucidate the incidence of HBC and its biological properties, histological specimens from 1010 breast cancer patients treated at Yokohama Minami Kyosai(More)
• Australasian J. Combinatorics
• 2006
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)
Polyomavirus JC (JCV) causes the human demyelinating disease, progressive multifocal leukoencephalopathy (PML). The recent demonstration of cases of PML in association with human T-lymphotropic virus type I (HTLV-I) infection prompted us to examine whether the HTLV-I-encoded regulatory protein Tax activates JCV transcription. By employing a dual luciferase(More)
In the peripheral blood leukocytes (PBLs) from the carriers of the human T-lymphotropic virus type-1 (HTLV-1) or the patients with adult T-cell leukemia (ATL), nuclear factor kappaB (NF-κB)-mediated antiapoptotic signals are constitutively activated primarily by the HTLV-1-encoded oncoprotein Tax. Tax interacts with the I κB kinase regulatory subunit NEMO(More)