PLANAR PACKING OF CYCLES AND UNICYCLIC GRAPHS

Agnieszka Gôrlich
2009 Demonstratio Mathematica  
We say that a graph G is packable into a complete graph K n if there are two edge-disjoint subgraphs of K n both isomorphic to G. It is equivalent to the existence of a permutation a of a vertex set in G such that if an edge xy belongs to E(G), then a(x)cr(y) does not belong to E(G). In 2002 Garcia et al. have shown that a non-star tree T is planary packable into a complete graph K n . In this paper we show that for any packable cycle C n except of the case n = 5 and n = 7 there exists a planar
more » ... packing into K n . We also generalize this result to certain classes of unicyclic graphs.
doi:10.1515/dema-2009-0402 fatcat:ptqhl4plerg7db7fm77o3azyb4