Moshe Rosenfeld - Academia.edu (original) (raw)

Papers by Moshe Rosenfeld

Discrete Mathematics & Theoretical Computer Science

Special issue PRIMA 2013 The prisms over cubic graphs are 4-regular graphs. The prisms over 3-con... more Special issue PRIMA 2013 The prisms over cubic graphs are 4-regular graphs. The prisms over 3-connected cubic graphs are Hamiltonian. In 1986 Brian Alspach and Moshe Rosenfeld conjectured that these prisms are Hamiltonian decomposable. In this paper we present a short survey of the status of this conjecture, various constructions proving that certain families of prisms over 3-connected cubic graphs are Hamiltonian decomposable. Among others, we prove that the prisms over cubic Halin graphs, cubic generalized Halin graphs of order 4k + 2 and other infinite sequences of cubic graphs are Hamiltonian decomposable.

Journal of Combinatorial Theory, Series B, Jun 1, 1974

In this paper we prove that every tournament T, with II _ 2k :.-28 vertices has an antidirected H... more In this paper we prove that every tournament T, with II _ 2k :.-28 vertices has an antidirected Hamiltonian circuit as was conjectured by Griinbaum [3]. We also investigate the number of distinct antidirected Hamiltonian paths and circuits in T, and obtain upper bounds for these numbers. DEFINITIONS AND NOTATION. The transitive tournament TT, is a tournament with vertices {al ,..., a,] and ai + aj iff i <,j. The vertices ai , 1 < i < 17, are called internal vertices. The tournaments Tzc and T," are the unique regular tournaments with three and five vertices, respectively. TTc is a tournament that can be defined as follows: its vertices are the elements (0, I,..., 6) of the finite field GF(7), and i-j iff .i-i is a quadratic element in GF(7).

Discrete Mathematics, Oct 1, 1990

Israel Journal of Mathematics, Mar 1, 1971

... OF TWO SIDED IDEALS IN B(H)* BY JOHN A. DYER, PASQUALE PORCELLI AND MOSHE ROSENFELD ABSTRACT ... more ... OF TWO SIDED IDEALS IN B(H)* BY JOHN A. DYER, PASQUALE PORCELLI AND MOSHE ROSENFELD ABSTRACT In this paper we prove that an element A ~ B(H) belongs to a proper two sided ideal in B(H) if and only if ~(A + T) N ~(T) ~ ~ VT~ B(H) ...

DIMACS series in discrete mathematics and theoretical computer science, Jun 26, 1991

Order, Feb 1, 2005

Let B k be the bipartite graph defined by the subsets of {1,. .. , 2k + 1} of size k and k + 1. W... more Let B k be the bipartite graph defined by the subsets of {1,. .. , 2k + 1} of size k and k + 1. We prove that the prism over B k is hamiltonian. We also show that B k has a closed spanning 2-trail.

Israel Journal of Mathematics, Oct 31, 2010

A polytope P with 2n vertices is called equipartite if for any partition of its vertex set into t... more A polytope P with 2n vertices is called equipartite if for any partition of its vertex set into two equal-size sets V 1 and V 2, there is an isometry of the polytope P that maps V 1 onto V 2. We prove that an equipartite polytope in ℝ d can have at most 2d+2 vertices. We show that this bound is sharp and identify all known equipartite polytopes in ℝ d . We conjecture that the list is complete.

Siam Journal on Control and Optimization, Jul 1, 1982

Electronic Notes in Discrete Mathematics, Mar 1, 2007

ABSTRACT

Ars Mathematica Contemporanea, Nov 10, 2008

Some problems become famous and attract attention while others collect dust on the shelf. Large c... more Some problems become famous and attract attention while others collect dust on the shelf. Large conferences are a great breeding ground for popularizing both old and new problems. In this note we present some off the shelf problems.

Discrete Mathematics, 1978

In this paper it is shown that the prisr~ eve: cyclically 4-connect simple 3-polytopes ndmit Hami... more In this paper it is shown that the prisr~ eve: cyclically 4-connect simple 3-polytopes ndmit Hamiltonian circuits. It is also shown that if P is a simple 3-polytopc all of whose faces are polygons with six sides or less than the prism over P admits a Hamiltonian circuit.

Journal of Combinatorial Theory, Series B, Feb 1, 1972

In this paper we present a short proof of Griinbaum's theorem concerning the existence of antidir... more In this paper we present a short proof of Griinbaum's theorem concerning the existence of antidirected Hamiltonian (ADH) paths in tournaments. We atso prove that, in every tournament T, with n > 12, there is an ADH path starting at any vertex.

Bulletin of The Australian Mathematical Society, Feb 1, 1984

Information Processing Letters, Dec 1, 2009

In 1987, Akers, Harel and Krishnamurthy proposed the star graph Σ(n) as a new topology for interc... more In 1987, Akers, Harel and Krishnamurthy proposed the star graph Σ(n) as a new topology for interconnection networks. Hamiltonian properties of these graphs have been investigated by several authors. In this paper, we prove that Σ(n) contains n/8 pairwise edge-disjoint Hamilton cycles when n is prime, and Ω(n/ log log n) such cycles for arbitrary n.

Siam Journal on Control and Optimization, Mar 1, 1978

Let A,B\{ {A,B} \}A,B be an infinite dimensional linear system where A is normal with compact resolve... more Let A,B\{ {A,B} \}A,B be an infinite dimensional linear system where A is normal with compact resolvent and the input space is finite dimensional. Then the controllability of A,B\{ {A,B} \}A,B implies the possibility of assigning an arbitrary finite set of poles to the transfer function of the closed loop system formed by means of suitable linear state feedback. Thus such systems can always be stabilized through state feedback.

Discrete Mathematics, Aug 1, 1973

Discrete Mathematics, Sep 1, 2015

We prove that every finite 3-colorable graph has an odd-distance faithful representation in the p... more We prove that every finite 3-colorable graph has an odd-distance faithful representation in the plane. In other words, we can draw it in the plane so that any two vertices are connected by an edge if and only if their distance is an odd integer.

Proceedings of the American Mathematical Society, 1970

A constructive method for obtaining graphs with a relatively large capacity is given. The method ... more A constructive method for obtaining graphs with a relatively large capacity is given. The method uses products of graphs.

Israel Journal of Mathematics, Sep 19, 2008

ABSTRACT

Discrete Mathematics & Theoretical Computer Science

Special issue PRIMA 2013 The prisms over cubic graphs are 4-regular graphs. The prisms over 3-con... more Special issue PRIMA 2013 The prisms over cubic graphs are 4-regular graphs. The prisms over 3-connected cubic graphs are Hamiltonian. In 1986 Brian Alspach and Moshe Rosenfeld conjectured that these prisms are Hamiltonian decomposable. In this paper we present a short survey of the status of this conjecture, various constructions proving that certain families of prisms over 3-connected cubic graphs are Hamiltonian decomposable. Among others, we prove that the prisms over cubic Halin graphs, cubic generalized Halin graphs of order 4k + 2 and other infinite sequences of cubic graphs are Hamiltonian decomposable.

Journal of Combinatorial Theory, Series B, Jun 1, 1974

In this paper we prove that every tournament T, with II _ 2k :.-28 vertices has an antidirected H... more In this paper we prove that every tournament T, with II _ 2k :.-28 vertices has an antidirected Hamiltonian circuit as was conjectured by Griinbaum [3]. We also investigate the number of distinct antidirected Hamiltonian paths and circuits in T, and obtain upper bounds for these numbers. DEFINITIONS AND NOTATION. The transitive tournament TT, is a tournament with vertices {al ,..., a,] and ai + aj iff i <,j. The vertices ai , 1 < i < 17, are called internal vertices. The tournaments Tzc and T," are the unique regular tournaments with three and five vertices, respectively. TTc is a tournament that can be defined as follows: its vertices are the elements (0, I,..., 6) of the finite field GF(7), and i-j iff .i-i is a quadratic element in GF(7).

Discrete Mathematics, Oct 1, 1990

Israel Journal of Mathematics, Mar 1, 1971

... OF TWO SIDED IDEALS IN B(H)* BY JOHN A. DYER, PASQUALE PORCELLI AND MOSHE ROSENFELD ABSTRACT ... more ... OF TWO SIDED IDEALS IN B(H)* BY JOHN A. DYER, PASQUALE PORCELLI AND MOSHE ROSENFELD ABSTRACT In this paper we prove that an element A ~ B(H) belongs to a proper two sided ideal in B(H) if and only if ~(A + T) N ~(T) ~ ~ VT~ B(H) ...

DIMACS series in discrete mathematics and theoretical computer science, Jun 26, 1991

Order, Feb 1, 2005

Let B k be the bipartite graph defined by the subsets of {1,. .. , 2k + 1} of size k and k + 1. W... more Let B k be the bipartite graph defined by the subsets of {1,. .. , 2k + 1} of size k and k + 1. We prove that the prism over B k is hamiltonian. We also show that B k has a closed spanning 2-trail.

Israel Journal of Mathematics, Oct 31, 2010

A polytope P with 2n vertices is called equipartite if for any partition of its vertex set into t... more A polytope P with 2n vertices is called equipartite if for any partition of its vertex set into two equal-size sets V 1 and V 2, there is an isometry of the polytope P that maps V 1 onto V 2. We prove that an equipartite polytope in ℝ d can have at most 2d+2 vertices. We show that this bound is sharp and identify all known equipartite polytopes in ℝ d . We conjecture that the list is complete.

Siam Journal on Control and Optimization, Jul 1, 1982

Electronic Notes in Discrete Mathematics, Mar 1, 2007

ABSTRACT

Ars Mathematica Contemporanea, Nov 10, 2008

Some problems become famous and attract attention while others collect dust on the shelf. Large c... more Some problems become famous and attract attention while others collect dust on the shelf. Large conferences are a great breeding ground for popularizing both old and new problems. In this note we present some off the shelf problems.

Discrete Mathematics, 1978

In this paper it is shown that the prisr~ eve: cyclically 4-connect simple 3-polytopes ndmit Hami... more In this paper it is shown that the prisr~ eve: cyclically 4-connect simple 3-polytopes ndmit Hamiltonian circuits. It is also shown that if P is a simple 3-polytopc all of whose faces are polygons with six sides or less than the prism over P admits a Hamiltonian circuit.

Journal of Combinatorial Theory, Series B, Feb 1, 1972

In this paper we present a short proof of Griinbaum's theorem concerning the existence of antidir... more In this paper we present a short proof of Griinbaum's theorem concerning the existence of antidirected Hamiltonian (ADH) paths in tournaments. We atso prove that, in every tournament T, with n > 12, there is an ADH path starting at any vertex.

Bulletin of The Australian Mathematical Society, Feb 1, 1984

Information Processing Letters, Dec 1, 2009

In 1987, Akers, Harel and Krishnamurthy proposed the star graph Σ(n) as a new topology for interc... more In 1987, Akers, Harel and Krishnamurthy proposed the star graph Σ(n) as a new topology for interconnection networks. Hamiltonian properties of these graphs have been investigated by several authors. In this paper, we prove that Σ(n) contains n/8 pairwise edge-disjoint Hamilton cycles when n is prime, and Ω(n/ log log n) such cycles for arbitrary n.

Siam Journal on Control and Optimization, Mar 1, 1978

Let A,B\{ {A,B} \}A,B be an infinite dimensional linear system where A is normal with compact resolve... more Let A,B\{ {A,B} \}A,B be an infinite dimensional linear system where A is normal with compact resolvent and the input space is finite dimensional. Then the controllability of A,B\{ {A,B} \}A,B implies the possibility of assigning an arbitrary finite set of poles to the transfer function of the closed loop system formed by means of suitable linear state feedback. Thus such systems can always be stabilized through state feedback.

Discrete Mathematics, Aug 1, 1973

Discrete Mathematics, Sep 1, 2015

We prove that every finite 3-colorable graph has an odd-distance faithful representation in the p... more We prove that every finite 3-colorable graph has an odd-distance faithful representation in the plane. In other words, we can draw it in the plane so that any two vertices are connected by an edge if and only if their distance is an odd integer.

Proceedings of the American Mathematical Society, 1970

A constructive method for obtaining graphs with a relatively large capacity is given. The method ... more A constructive method for obtaining graphs with a relatively large capacity is given. The method uses products of graphs.

Israel Journal of Mathematics, Sep 19, 2008

ABSTRACT