Seiya Negami - Academia.edu (original) (raw)

Papers by Seiya Negami

In this paper, we shall prove that every 5-connected triangulation of the Klein bottle has a Hami... more In this paper, we shall prove that every 5-connected triangulation of the Klein bottle has a Hamilton cycle, which is contractible.

An optimal 1-planar graph G is a graph which can be drawn on the sphere, admitting at most one cr... more An optimal 1-planar graph G is a graph which can be drawn on the sphere, admitting at most one crossing point on each edge with |E(G)|=4|V(G)|-8. Suzuki has already proved that there exists an optimal 1-planar graph which can be embedded on the orientable closed surface of genus g as a triangulation for any positive integer g, and has shown that there exists no such graph for the non-orientable closed surfaces of genus 1, 2 and 3. We shall show the non-existence of such a graph for genus 4, carrying out a computer experiment.

ABSTRACT A graph G is said to be d-distinguishing colorable if there is a d-coloring of G such th... more ABSTRACT A graph G is said to be d-distinguishing colorable if there is a d-coloring of G such that no automorphism of G except the identity map preserves colors. We shall prove that every 3-connected planar graph is 5-distinguishing colorable except K 2,2,2 and C 6 +K 2 ¯ and that every 3-connected bipartite planar graph is 3-distinguishing colorable except Q 3 and R(Q 3 ).

We shall show that any projective-planar double covering of a 3connected graph is planar, discuss... more We shall show that any projective-planar double covering of a 3connected graph is planar, discussing structures of double covering of planar graphs algebraically and combinatorially.

This paper is related to the third author's previous result on the existence of volume polynomial... more This paper is related to the third author's previous result on the existence of volume polynomials for a given polyhedron having only triangular faces. We simplify his original proof in the case when the polyhedron is homeomorphic to the 2-sphere. Our approach exploits the fact that any such polyhedron contains a so-called clean vertex -that is, a vertex not incident with any nonfacial cycle composed of 3 edges. This fact appears as one of the main results of the article. Also, we characterize triangulations reducible to a tetrahedron by repeatedly removing 3-valent vertices, and estimate the degree of volume polynomials. We address the torus case too. MSC 2000: 52B05 (primary); 51M25, 57M15, 57Q15 (secondary)

Transactions of the American Mathematical Society, 1985

A method to simplify 3-bridge projections of links and knots, called a wave move, is discussed in... more A method to simplify 3-bridge projections of links and knots, called a wave move, is discussed in general situation and it is shown what kind of properties of 3-bridge links and knots can be recognized from their projections by wave moves. In particular, it will be proved that every 3-bridge projection of a splittable link or a trivial knot can be transformed into a disconnected one or a hexagon, respectively, by a finite sequence of wave moves. As its translation via the concept of 2-fold branched coverings of S3, it follows that every genus 2 Heegaard diagram of S2 x S2 # L(p, q) or S3 can be transformed into one of specific standard forms by a finite sequence of operations also called wave moves.

Journal of Combinatorial Theory, Series B, 1997

Journal of Combinatorial Theory, Series B, 1999

We show how to construct all the graphs that can be embedded on both the torus and the Klein bott... more We show how to construct all the graphs that can be embedded on both the torus and the Klein bottle as their triangulations.

Journal of Combinatorial Theory, Series B, 1993

Journal of Combinatorial Theory, Series B, 2011

A graph with at least 2k+2 vertices is said to be k-extendable if any independent set of k edges ... more A graph with at least 2k+2 vertices is said to be k-extendable if any independent set of k edges in it extends to a perfect matching. We shall show that every 5-connected graph G of even order embedded on a closed surface F2, except the sphere, is 2-extendable if ρ(G)⩾7−2χ(F2), where ρ(G) stands for the representativity of G on F2

The distinguishing number is a combinatorial invariant defined for an abstract graph, concerning ... more The distinguishing number is a combinatorial invariant defined for an abstract graph, concerning the symmetry of graphs as follows. Let G be a graph and c : V (G) → {1, 2, ..., d} an assignment of labels to the vertices of G. Such a labeling c is called a d-distinguishing labeling of G if no automorphism of G other than the identity map preserves the labels given by c. A graph G is said to be d-distinguishable if G admits a d-distinguishing labeling. The distinguishing number of G is defined as the minimum number d such that G is d-distinguishable and is denoted by D (G). For examples, the distinguishing number of a complete graph K n is D(K n ) = n.

In this paper, we shall prove that every 5-connected triangulation of the Klein bottle has a Hami... more In this paper, we shall prove that every 5-connected triangulation of the Klein bottle has a Hamilton cycle, which is contractible.

An optimal 1-planar graph G is a graph which can be drawn on the sphere, admitting at most one cr... more An optimal 1-planar graph G is a graph which can be drawn on the sphere, admitting at most one crossing point on each edge with |E(G)|=4|V(G)|-8. Suzuki has already proved that there exists an optimal 1-planar graph which can be embedded on the orientable closed surface of genus g as a triangulation for any positive integer g, and has shown that there exists no such graph for the non-orientable closed surfaces of genus 1, 2 and 3. We shall show the non-existence of such a graph for genus 4, carrying out a computer experiment.

ABSTRACT A graph G is said to be d-distinguishing colorable if there is a d-coloring of G such th... more ABSTRACT A graph G is said to be d-distinguishing colorable if there is a d-coloring of G such that no automorphism of G except the identity map preserves colors. We shall prove that every 3-connected planar graph is 5-distinguishing colorable except K 2,2,2 and C 6 +K 2 ¯ and that every 3-connected bipartite planar graph is 3-distinguishing colorable except Q 3 and R(Q 3 ).

We shall show that any projective-planar double covering of a 3connected graph is planar, discuss... more We shall show that any projective-planar double covering of a 3connected graph is planar, discussing structures of double covering of planar graphs algebraically and combinatorially.

This paper is related to the third author's previous result on the existence of volume polynomial... more This paper is related to the third author's previous result on the existence of volume polynomials for a given polyhedron having only triangular faces. We simplify his original proof in the case when the polyhedron is homeomorphic to the 2-sphere. Our approach exploits the fact that any such polyhedron contains a so-called clean vertex -that is, a vertex not incident with any nonfacial cycle composed of 3 edges. This fact appears as one of the main results of the article. Also, we characterize triangulations reducible to a tetrahedron by repeatedly removing 3-valent vertices, and estimate the degree of volume polynomials. We address the torus case too. MSC 2000: 52B05 (primary); 51M25, 57M15, 57Q15 (secondary)

Transactions of the American Mathematical Society, 1985

A method to simplify 3-bridge projections of links and knots, called a wave move, is discussed in... more A method to simplify 3-bridge projections of links and knots, called a wave move, is discussed in general situation and it is shown what kind of properties of 3-bridge links and knots can be recognized from their projections by wave moves. In particular, it will be proved that every 3-bridge projection of a splittable link or a trivial knot can be transformed into a disconnected one or a hexagon, respectively, by a finite sequence of wave moves. As its translation via the concept of 2-fold branched coverings of S3, it follows that every genus 2 Heegaard diagram of S2 x S2 # L(p, q) or S3 can be transformed into one of specific standard forms by a finite sequence of operations also called wave moves.

Journal of Combinatorial Theory, Series B, 1997

Journal of Combinatorial Theory, Series B, 1999

We show how to construct all the graphs that can be embedded on both the torus and the Klein bott... more We show how to construct all the graphs that can be embedded on both the torus and the Klein bottle as their triangulations.

Journal of Combinatorial Theory, Series B, 1993

Journal of Combinatorial Theory, Series B, 2011

A graph with at least 2k+2 vertices is said to be k-extendable if any independent set of k edges ... more A graph with at least 2k+2 vertices is said to be k-extendable if any independent set of k edges in it extends to a perfect matching. We shall show that every 5-connected graph G of even order embedded on a closed surface F2, except the sphere, is 2-extendable if ρ(G)⩾7−2χ(F2), where ρ(G) stands for the representativity of G on F2

The distinguishing number is a combinatorial invariant defined for an abstract graph, concerning ... more The distinguishing number is a combinatorial invariant defined for an abstract graph, concerning the symmetry of graphs as follows. Let G be a graph and c : V (G) → {1, 2, ..., d} an assignment of labels to the vertices of G. Such a labeling c is called a d-distinguishing labeling of G if no automorphism of G other than the identity map preserves the labels given by c. A graph G is said to be d-distinguishable if G admits a d-distinguishing labeling. The distinguishing number of G is defined as the minimum number d such that G is d-distinguishable and is denoted by D (G). For examples, the distinguishing number of a complete graph K n is D(K n ) = n.