Problem of the Week
Hilton Memorial Lecture
Circles (or “cycles”) are a fundamental structure of graphs. Problems of shortest and longest circles, for instance, or circles through specified vertices, are standard topics of investigation. In signed graphs, where each edge is signed positive or negative, circle problems become much richer, because the structural significance differs greatly depending on the sign of the circle (which is the product of its edge signs). I will discuss some circle properties in graphs and signed graphs with an emphasis on open problems in the latter.