At the previous seminar we have discussed a construction that provides infinitely many counterexamples to Tutteâ€™s conjecture. All such counterexamples have an essential edge 3-cut. Therefore a natural question arises as to whether Tutteâ€™s conjecture is true for graphs without essential edge 3-cuts. We will show that Tutteâ€™s conjecture is not true even for graphs without essential edge 3-cuts. Namely, we will describe some constructions providing infinitely many counterexamples to the conjecture without essential edge 3-cuts.

We will also discuss some known conjectures and put forward some new conjectures and problems along this line.

*
Although this seminar is a continuation of the previous one,
the material of this seminar can be understood without the
knowledge of the previously discussed material. *

Graduate students from all mathematical areas are very welcome.

The main prerequisite to this talk is the desire to understand.