Mod (2p + 1)-Orientations and $K_{1,2p+1}$-Decompositions
Hong‐Jian Lai · SIAM Journal on Discrete Mathematics · 2007
In this paper, we establish an equivalence between the contractible graphs with respect to the mod $(2p+1)$-orientability and the graphs with $K_{1, 2p+1}$-decompositions. This is applied to disprove a conjecture proposed by Barat and Thomassen that every 4-edge-connected simple planar graph G with $|E(G)|\equiv 0$ (mod 3) has a claw decomposition.