Decompositions and packings in truncated triangulations
Michael Muzheve (kumtm000@tamuk.edu)
We study decompositions and packings in truncated triangulations G T△ obtained from simple connected plane graphs G with minimum degree two. We show G T△ is a 3-connected cubic planar graph with at least 2|E(G)|² - 2|E(G)| + 1 perfect matchings, a Λ-factor, and can be decomposed into a union of C₆'s and K₂'s if G is bipartite. Additionally, we show that G T△ is hamiltonian if G is bipartite with a dominating path P satisfying, for any e = xy ∉ E(P) exactly one of x and y is in V(P). We also prov