Splitting cubic circle graphs
Copyright policy )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.
18 pages, 15 figures
- Lafayette College United States
Graph representations (geometric and intersection representations, etc.), circle graph, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), regular graph, QA1-939, FOS: Mathematics, Mathematics - Combinatorics, split decomposition, Combinatorics (math.CO), Mathematics
Graph representations (geometric and intersection representations, etc.), circle graph, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), regular graph, QA1-939, FOS: Mathematics, Mathematics - Combinatorics, split decomposition, Combinatorics (math.CO), Mathematics
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