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2-factor 3-connected 3-cycle adjacent algorithm Anne Penfold Applications automorphism bipartite block-orbits Bruhat order coloring Combinatorial Designs Combinatorics complete graph Computer conference configuration consider construction contradiction Corollary counterchordal cover pebbling number cover-solvable cyclic decomposition define delete denote diameter difference digraph Discrete Math Discrete Mathematics disjoint dominating set elements exactly Example exists exponent terrace finite G-orbit girth graph G Graph Theory grid graph Hamiltonian circuit Hence hexagon triple system Institute of Combinatorics integer involution isomorphic Kirkman Medals L-coloring Lemma Let G logarithmic terrace matrix maximal Medal neighbour non-leaves Note number of vertices ordered pairs P3-equipackable paper parity partition path Petersen Graph problem Proof Ralph Faudree ramsey numbers RBIBD result selfrepeats sequence sparsely dominated Steiner triple system stems subgraph system of order Theorem total labeling total perfect code tournament University upper vertex set vertices of order wheel graph Zp-i