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Articles 1 - 16 of 16
Full-Text Articles in Physical Sciences and Mathematics
Spatial Graphs With Local Knots, Ramin Naimi, Erica Flapan, Blake Mellor
Spatial Graphs With Local Knots, Ramin Naimi, Erica Flapan, Blake Mellor
Ramin Naimi
It is shown that for any locally knotted edge of a 3-connected graph in $S^3$, there is a ball that contains all of the local knots of that edge and is unique up to an isotopy setwise fixing the graph. This result is applied to the study of topological symmetry groups of graphs embedded in $S^3$.
Induced Subgraphs Of Johnson Graphs, Ramin Naimi, Jeffrey Shaw
Induced Subgraphs Of Johnson Graphs, Ramin Naimi, Jeffrey Shaw
Ramin Naimi
The Johnson graph J(n,N) is defined as the graph whose vertices are the n-subsets of the set {1,2,...,N}, where two vertices are adjacent if they share exactly n - 1 elements. Unlike Johnson graphs, induced subgraphs of Johnson graphs (JIS for short) do not seem to have been studied before. We give some necessary conditions and some sufficient conditions for a graph to be JIS, including: in a JIS graph, any two maximal cliques share at most two vertices; all trees, cycles, and complete graphs are JIS; disjoint unions and Cartesian products of JIS graphs are JIS; every JIS graph …
Complete Graphs Whose Topological Symmetry Groups Are Polyhedral, Ramin Naimi, Erica Flapan, Blake Mellor
Complete Graphs Whose Topological Symmetry Groups Are Polyhedral, Ramin Naimi, Erica Flapan, Blake Mellor
Ramin Naimi
We determine for which $m$, the complete graph $K_m$ has an embedding in $S^3$ whose topological symmetry group is isomorphic to one of the polyhedral groups: $A_4$, $A_5$, or $S_4$.
List Coloring And N-Monophilic Graphs, Ramin Naimi, Radoslav Kirov
List Coloring And N-Monophilic Graphs, Ramin Naimi, Radoslav Kirov
Ramin Naimi
In 1990, Kostochka and Sidorenko proposed studying the smallest number of list-colorings of a graph G among all assignments of lists of a given size n to its vertices. We say a graph G is n-monophilic if this number is minimized when identical n-color lists are assigned to all vertices of G. Kostochka and Sidorenko observed that all chordal graphs are n-monophilic for all n. Donner (1992) showed that every graph is n-monophilic for all sufficiently large n. We prove that all cycles are n-monophilic for all n; we give a complete characterization of 2-monophilic graphs (which turns out to …
Topology Explains Why Automobile Shades Fold Oddly, Ramin Naimi, Curtis Feist
Topology Explains Why Automobile Shades Fold Oddly, Ramin Naimi, Curtis Feist
Ramin Naimi
We use braids and linking number to explain why automobile shades fold into an odd number of loops.
Intrinsic Linking And Knotting Are Arbitrarily Complex, Ramin Naimi, Erica Flapan, Blake Mellor
Intrinsic Linking And Knotting Are Arbitrarily Complex, Ramin Naimi, Erica Flapan, Blake Mellor
Ramin Naimi
We show that, given any $n$ and $\alpha$, every embedding of any sufficiently large complete graph in $\mathbb{R}^3$ contains an oriented link with components $Q_1$, ..., $Q_n$ such that for every $i\not =j$, $|\lk(Q_i,Q_j)|\geq\alpha$ and $|a_2(Q_i)|\geq\alpha$, where $a_{2}(Q_i)$ denotes the second coefficient of the Conway polynomial of $Q_i$.
Maximizing The Chances Of A Color Match, Ramin Naimi, Roberto Pelayo
Maximizing The Chances Of A Color Match, Ramin Naimi, Roberto Pelayo
Ramin Naimi
No abstract provided.
Topological Symmetry Groups Of Embedded Graphs In The 3-Sphere, Ramin Naimi, Erica Flapan, James Pommersheim, Harry Tomvakis
Topological Symmetry Groups Of Embedded Graphs In The 3-Sphere, Ramin Naimi, Erica Flapan, James Pommersheim, Harry Tomvakis
Ramin Naimi
No abstract provided.
Almost Alternating Harmonic Series, Ramin Naimi, Curtis Fesit
Almost Alternating Harmonic Series, Ramin Naimi, Curtis Fesit
Ramin Naimi
No abstract provided.
The Y-Triangle Move Does Not Preserve Intrinsic Knottedness, Ramin Naimi, Erica Flapan
The Y-Triangle Move Does Not Preserve Intrinsic Knottedness, Ramin Naimi, Erica Flapan
Ramin Naimi
We answer the question "Does the Y-triangle move preserve intrinsic knottedness?" in the negative by giving an example of a graph that is obtained from the intrinsically knotted graph K_7 by triangle-Y and Y-triangle moves but is not intrinsically knotted.
Intrinsically Triple Linked Complete Graphs, Ramin Naimi, Erica Flapan, James Pommersheim
Intrinsically Triple Linked Complete Graphs, Ramin Naimi, Erica Flapan, James Pommersheim
Ramin Naimi
No abstract provided.
Intrinsically N-Linked Graphs, Ramin Naimi, Erica Flapan, Joel Foisy, James Pommersheim
Intrinsically N-Linked Graphs, Ramin Naimi, Erica Flapan, Joel Foisy, James Pommersheim
Ramin Naimi
No abstract provided.
Essential Laminations In Graph Manifolds, Ramin Naimi, Mark Brittenham, Rachel Roberts
Essential Laminations In Graph Manifolds, Ramin Naimi, Mark Brittenham, Rachel Roberts
Ramin Naimi
No abstract provided.
Constructing Essential Laminations In 2-Bridge Knot Surgered 3-Manifolds, Ramin Naimi
Constructing Essential Laminations In 2-Bridge Knot Surgered 3-Manifolds, Ramin Naimi
Ramin Naimi
A nontrivial knot that can be drawn with only two relative maxima in the vertical direction is called a 2-bridge knot, and one that can be drawn on a torus is called a torus knot. Loosely speaking, a lamination in a manifold M is a foliation of M, except that it can have a nonempty open complement in M, and very loosely speaking, the lamination is essential if each leaf of it L is incompressible, i.e. inclusion of L into M induces an injective homomorphism from π1(L) into π1(M). Our main result is: Theorem 2. Every 3-manifold obtained by surgery …
Foliations Transverse To Fibers Of Seifert Manifolds, Ramin Naimi
Foliations Transverse To Fibers Of Seifert Manifolds, Ramin Naimi
Ramin Naimi
No abstract provided.
Constructing Essential Laminations In 3-Manifolds Obtained By Surgery On 2-Bridge Knots, Ramin Naimi
Constructing Essential Laminations In 3-Manifolds Obtained By Surgery On 2-Bridge Knots, Ramin Naimi
Ramin Naimi
No abstract provided.