4 research outputs found
Splitting cubic circle graphs
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.Comment: 18 pages, 15 figure
Splitting Cubic Circle Graphs
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, K4 and K3,3 are the only 3-connected, 3-regular circle graphs