Cyclic connectivity classes of directed graphs.
Cyclic Crystallizations of Spheres.
Cyclic decompositions of complete graphs into spanning trees
We examine decompositions of complete graphs with an even number of vertices, , into n isomorphic spanning trees. While methods of such decompositions into symmetric trees have been known, we develop here a more general method based on a new type of vertex labelling, called flexible q-labelling. This labelling is a generalization of labellings introduced by Rosa and Eldergill.
Cyclic labellings with constraints at two distances.
Cyclic partitions of complete uniform hypergraphs.
Cyclic projective planes and Wada dessins.
Cyclic sieving phenomenon in non-crossing connected graphs.
Cyclically 5-edge connected non-bicritical critical snarks
Snarks are bridgeless cubic graphs with chromatic index χ' = 4. A snark G is called critical if χ'(G-{v,w}) = 3, for any two adjacent vertices v and w. For any k ≥ 2 we construct cyclically 5-edge connected critical snarks G having an independent set I of at least k vertices such that χ'(G-I) = 4. For k = 2 this solves a problem of Nedela and Skoviera [6].
Cyclically k-partite digraphs and k-kernels
Let D be a digraph, V(D) and A(D) will denote the sets of vertices and arcs of D, respectively. A (k,l)-kernel N of D is a k-independent set of vertices (if u,v ∈ N then d(u,v) ≥ k) and l-absorbent (if u ∈ V(D)-N then there exists v ∈ N such that d(u,v) ≤ l). A k-kernel is a (k,k-1)-kernel. A digraph D is cyclically k-partite if there exists a partition of V(D) such that every arc in D is a (mod k). We give a characterization for an unilateral digraph to be cyclically k-partite through the lengths...
Cyclicity of a complete 3-equipartite graph