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bio website york.cuny.edu/~malk
location New York, NY
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visits member for 3 years, 8 months
seen Apr 2 at 18:18

I am a mathematician interested in geometry, combinatorics, mathematical modeling, and mathematics education.


Apr
2
answered Find a voting system - possibly Schulze Method
Mar
22
answered Maximum number of pipes used to construct the polygon
Mar
20
comment showing that all convex polehedron graphs are 3-connected
Typo in above in my statement of Steinitz's Theorem: A graph is 3-polytopal if and only it is planar and 3-connected.
Mar
20
comment showing that all convex polehedron graphs are 3-connected
Tutte tended to use somewhat different terminology from some other authors, and I don't know his definitions here. The now "standard" approach to Steinitz's Theorem: A graph is 3-polytopal if and only if it is 3-connected is described in the books of polytopes by Grünbaum and Ziegler. Their approach allows graphs to be 4 or 5-connected but also 3-connected. Some 3-connected graphs are not 4-connected or 5-connected. The only proof I know of that 3-polytopes are 3-connected uses a theorem of M. Balinksi that the graphs of d-polytopes are d-connected.
Mar
20
comment showing that all convex polehedron graphs are 3-connected
The edge-vertex graphs of some 3-dimensional convex polytopes are more than 3-connected. For example the regular icosahedron's graph is 5-connected. One approach to 3-connectedness is to say that every pair of distinct vertices u and v can be joined by at least 3 paths whose only vertices in common are u and v. On the icosahedron for any pair of distinct vertices there are 5 such paths so the icosahedron is 5-connected.
Mar
20
comment Proving the easy direction of Steinitz's theorem.
One approach to answering this is to use facts about graphs of (convex) d-polytopes when d is 3 or more.
Sep
29
comment Recommend an intro to binary embedding algorithm in Graph Theory
I don't understand what you mean by a "binary embedding of a tree." There are many papers about embedding binary trees into graphs. For example, embedding binary trees into d-dimensional hypercubes.
Sep
29
answered Show that $f(2n)= f(n+1)^2 - f(n-1)^2$
Sep
29
answered Visualising finite fields
Sep
29
answered Is differential geometry useful for algebra?
Sep
29
answered equation representing 2 straight lines
Sep
29
answered If a point has no dimension and no area how can there be space?
Sep
2
answered Looking for a significant example that highlights the suboptimality of the greedy algorithms
Aug
20
awarded  Yearling
Jul
4
comment A parametrization of the sides of right triangles
Hint: Look into what are called Pythagorean Triples.
Jun
17
comment Polytopes characterization in $\mathbb R^n$
Many issues related to polytopes are discussed in Branko Grunbaum's excellent book Convex Polytopes.
Jun
3
answered Symmetries of a graph
May
31
awarded  Good Answer
May
7
comment Applications of design theory
The CRC Handbook of Combinatorial Designs edited by Charles Colbourn and Jeffrey Dinitz has lots of examples of applications of various kinds of designs. When one has a specific application sometimes one can consult "tables of designs" and find something that helps. However, often finding the design for a specific application is like looking for a needle in a haystack.
May
4
answered Exceptional books on real world applications of graph theory.