Open Problem Garden

Problem   What is the maximum number of colours needed to colour countries such that no two countries sharing a common border have the same colour in the case where each country consists of one region on earth and one region on the moon ?

Conjecture   If has at most edge-disjoint triangles, then there is a set of edges whose deletion destroys every triangle.

Conjecture   If is a simple triangle-free graph, then there is a set of at most edges whose deletion destroys every odd cycle.