On the Cycle Spectrum of Cubic Hamiltonian Graphs

The Cycle Spectrum of Claw-free Hamiltonian Graphs

“…Sufficient conditions for hamiltonicity of claw-free graphs [3,12] or sufficient conditions for hamiltonicity that involve degree conditions on induced claws [1,2] have been proposed. The cycle spectrum of sparse claw-free hamiltonian graphs was considered [11]. Cycle lengths in hamiltonian graphs with few vertices of large degree [4,6,[8][9][10] and degree conditions for (sub)pancyclism of claw-free graphs [5,13] were studied.…”

Constructions, classifications and embeddings of abstract unitals

“…By switching the two colors in γ we obtain a new edge 3-coloring of Γ which is equivalent to the original one if and only if v = 2m + 1. Recently, cycles in cubic graphs, their length and especially Hamiltonian cycles are a central and well-studied topic in graph theory, see [11,41,17,15]. The authors of this paper are not aware of any results which could help to describe the structure of edge 3-colored cubic graphs, which occur as T b for a Steiner triples system T.…”

“…Listing 4.3). Listing 4.3: P4M unital with 4 collinear full points u := P4MAbstractUnital( 138 );; b1 := [ 16,20,22,34,62 ];; b2 := [ 6,10,27,35,41 ];; fullpts := FullPointsOfUnitalsBlocks( u, b1, b2 ); ## [ 5,30,37,42,61 ] ForAny( BlocksOfUnital( u ), x -> IsSubset( x, fullpts ) ); ## false First( BlocksOfUnital( u ),…”