A sufficient condition for dominating cycles

Two sufficient conditions for dominating cycles

A cycle C of a graph G is dominating if each component of GnC is edgeless. In the paper, we will give two sufficient conditions for each longest cycle of a 3-connected graph to be a dominating cycle. 2005 Wiley Periodicals, Inc. J Graph Theory 49: 135–150, 2005

Two Sufficient Conditions for Hamilton and Dominating Cycles

We prove that ifG is a 2-connect graph of size q the number of edges andminimumdegree δwith δ ≥ 2q/3 /12−1/2, where 11 when δ 2 and 31 when δ ≥ 3, then each longest cycle in G is a dominating cycle. The exact analog of this theorem for Hamilton cycles follows easily from two known results according to Dirac and Nash-Williams: each graph with δ ≥ q 5/4 − 1/2 is hamiltonian. Both results are shar...

A sufficient condition for Hamilton cycles in bipartite tournaments

A sufficient condition for Hamiltonian cycles in bipartite tournaments

We prove a new sufficient conditi()n on degrees for a bipartite tournament to be Hamiltonian, that is, if an n x n bipartite tournament T satisfies the condition dT(u) + dj;(v) ~ n 1 whenever uv is an arc of T, then T is Hamiltonian, except for two exceptional graphs. This result is shown to be best possible in a sense. T(X, Y, E) denotes a bipartite tournament with bipartition (X, Y) and verte...

A Sharp Sufficient Condition for Sparsity Pattern Recovery

Sufficient number of linear and noisy measurements for exact and approximate sparsity pattern/support set recovery in the high dimensional setting is derived. Although this problem as been addressed in the recent literature, there is still considerable gaps between those results and the exact limits of the perfect support set recovery. To reduce this gap, in this paper, the sufficient con...