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05-XX Combinatorics

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Cyclically k-partite digraphs and k-kernels

Hortensia Galeana-Sánchez, César Hernández-Cruz (2011)

Discussiones Mathematicae Graph Theory

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 ${V_{i}}_{i = 0}^{k - 1}$ of V(D) such that every arc in D is a $V_{i} V_{i + 1} - a r c$ (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

Bohdan Zelinka (1985)

Archivum Mathematicum

Cyclotomy and complementary difference sets

G. Szekeres (1971)

Acta Arithmetica

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