Hi again! This is a list of some of my favorite open problems. Those with the symbol 🌱 next to them are, to my knowledge, mine.
I welcome any corrections, ideas, or opportunities for collaboration!
Rigidity Theory
- 🌱 What are the rigid graphs whose complement is also rigid? Note that by Laman's Theorem, such a graph must have at least 8 vertices.
It may be advantageous to consider minimally rigid graphs.
- 🌱 For k-vertex/edge (global) rigidity, what are the graphs G so that all minors of G maintain the given rigidity property?
- 🌱 What are the minimally rigid graphs in \mathbb{R}^3 for which the deletion of a single vertex yields a minimally rigid graph in \mathbb{R}^2?
Do such graphs exist?
Topological + Geometric Graph Theory
- Is every arrangement graph of a set of great circles 3-colorable? Given that Hadwiger's conjecture holds for n=4, showing that such graphs have
no minor of chromatic number 4 would resolve this question.
Read more here
(Hyper)Graph Theory
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