Decomposition of Circulants into Antidirected Hamilton Cycles
نویسندگان
چکیده
Let G = Gn(a1, a2, ..., ak) denote a directed circulant graph of order n with k pairwise distinct jumps [1]. Antidirected Hamilton cycle in G is a cycle of n arcs that does not contain induced directed path P2. Let C 1 G, C 2 G, ..., C k G be pairwise arc-disjoint antidirected Hamilton cycles in G, each composed of exactly two distinct jumps. We give the necessary and sufficient conditions for G, so it can be completely decomposed into C G, C 2 G, ..., C k G. Antidirected Hamilton cycles were studied in respect to the special families of digraphs, e.g., [2-4]. In [2] we studied the necessary and sufficient conditions for the existence of an antidirected Hamilton cycle in Gn(a1, a2, ..., ak). The following was obtained based on that.
منابع مشابه
Arbitrary Orientations of Hamilton Cycles in Digraphs
Let n be sufficiently large and suppose that G is a digraph on n vertices where every vertex has inand outdegree at least n/2. We show that G contains every orientation of a Hamilton cycle except, possibly, the antidirected one. The antidirected case was settled by DeBiasio and Molla, where the threshold is n/2 + 1. Our result is best possible and improves on an approximate result by Häggkvist ...
متن کاملPerfect 1-Factorisations of Circulants with Small Degree
A 1-factorisation of a graph G is a decomposition of G into edge-disjoint 1-factors (perfect matchings), and a perfect 1-factorisation is a 1-factorisation in which the union of any two of the 1-factors is a Hamilton cycle. We consider the problem of the existence of perfect 1-factorisations of even order circulant graphs with small degree. In particular, we characterise the 3-regular circulant...
متن کاملSymmetric Hamilton Cycle Decompositions of Complete Graphs Minus a 1-Factor
Let n ≥ 2 be an integer. The complete graph Kn with a 1-factor F removed has a decomposition into Hamilton cycles if and only if n is even. We show that Kn − F has a decomposition into Hamilton cycles which are symmetric with respect to the 1-factor F if and only if n ≡ 2, 4 mod 8. We also show that the complete bipartite graph Kn,n has a symmetric Hamilton cycle decomposition if and only if n ...
متن کاملHamilton cycle decompositions of k-uniform k-partite hypergraphs
Let m ≥ 2 and k ≥ 2 be integers. We show that K k×m has a decomposition into Hamilton cycles of Kierstead-Katona type if k | m. We also show that K (3) 3×m − T has a decomposition into Hamilton cycles where T is a 1-factor if and only if 3 m and m = 4. We introduce a notion of symmetry and comment on the existence of symmetric Hamilton cycle decompositions of K (k) k×m.
متن کاملProof of the 1-factorization and Hamilton Decomposition Conjectures Ii: the Bipartite Case
In a sequence of four papers, we prove the following results (via a unified approach) for all sufficiently large n: (i) [1-factorization conjecture] Suppose that n is even and D ≥ 2dn/4e − 1. Then every D-regular graph G on n vertices has a decomposition into perfect matchings. Equivalently, χ′(G) = D. (ii) [Hamilton decomposition conjecture] Suppose that D ≥ bn/2c. Then every D-regular graph G...
متن کامل