Peter Hamburger

Doodles and doilies, non-simple symmetric Venn diagrams

In this paper, we create and implement a method to construct a non-simple, symmetric 11-Venn diagram. By doing this we answer a question of Grunbaum. Daniel Kleitmans mathematics seems to be remote from this area, but in fact, his results inspired this solution, which holds promise of settling the general case for all prime numbers, and the promise to find simple doilies with 11 and more curves as well.

Kneser Representations of Graphs

The Kneser graph

Venn said it couldn't be done.

K_{n:k}

Routing sets in the integer lattice

for positive integers

Simple, Reducible Venn Diagrams on Five Curves and Hamiltonian Cycles

n\ge k

Symmetric Venn Diagrams in the Plane: The Art of Assigning a Binary Bit String Code to Planar Regions Using Curves

has as its vertex set the

Analysis of Venn Diagrams Using Cycles in Graphs

k

Regular Honest Graphs, Isoperimetric Numbers, and Bisection of Weighted Graphs

-element subsets of some

Hypercube subgraphs with local detours

n

Edge Disjoint Paths of Increasing Order in Complete Bipartite Graphs

-set, with disjoint sets being adjacent. Every finite simple graph can be found as an induced subgraph of some Kneser graph; this article explores some questions arising from that fact.