Splitting cubic circle graphs
arXiv:1504.01143 · doi:10.7151/dmgt.1894
Abstract
We show that every 3-regular circle graph has at least two pairs of twin vertices; consequently no such graph is prime with respect to the split decomposition. We also deduce that up to isomorphism, K_4 and K_{3,3} are the only 3-connected, 3-regular circle graphs.
arXiv comment18 pages, 15 figures