Mathematics Seminar - 9 November 2012
Lowell Thomas Room 006, 3:30 PM
Some Classes of Graphs that are Close to being Cycle-free
A graph is almost series-parallel if there is some edge that one can add to the graph and then contract out to leave a series-parallel graph, that is, a graph with no K4-minor. In this talk, we find the full list of excluded minors for the class of graphs that are almost series-parallel. We also obtain the corresponding result for the class of graphs such that uncontracting an edge and then deleting the uncontracted edge produces a series-parallel graph.
A notable feature of a 3-connected almost series-parallel graph is that it has two vertices whose removal leaves a tree. This motivates consideration of those graphs for which there are two vertices whose removal is cycle-free. We find the full list of excluded minors for the class of graphs that have a set of at most two vertices whose removal is cycle-free.
This talk is based on Work with James Oxley of Lousiana State University.
Refreshments will be served.