A Chvátal-Erdös condition for (1,1)-factors in digraphs
نویسندگان
چکیده
منابع مشابه
Chvátal-Erdös condition and pancyclism
The well-known Chvátal-Erdős theorem states that if the stability number α of a graph G is not greater than its connectivity then G is hamiltonian. In 1974 Erdős showed that if, additionally, the order of the graph is sufficiently large with respect to α, then G is pancyclic. His proof is based on the properties of cycle-complete graph Ramsey numbers. In this paper we show that a similar result...
متن کاملPaths partition with prescribed beginnings in digraphs: A Chvátal-Erdös condition approach
A digraph D verifies the Chvátal-Erdős conditions if α(D) ≤ κ(D), where α(D) is the stability of D and κ(D) is its vertex-connectivity. Related to the Gallai-Milgram Theorem ([5]), we raise in this context the following conjecture. For every set of α = α(D) vertices {x1, . . . , xα}, there exists a vertex-partition of D into directed paths {P1, . . . , Pα} such that Pi begins at xi for all i. T...
متن کاملChvátal-Erdös type theorems
The Chvátal-Erdös theorems imply that if G is a graph of order n ≥ 3 with κ(G) ≥ α(G), then G is hamiltonian, and if κ(G) > α(G), then G is hamiltonian-connected. We generalize these results by replacing the connectivity and independence number conditions with a weaker minimum degree and independence number condition in the presence of sufficient connectivity. More specifically, it is noted tha...
متن کاملThe Existence of a 2-Factor in a Graph Satisfying the Local Chvátal-Erdös Condition
The well-known Chvátal–Erdős Theorem states that every graph G of order at least three with α(G) ≤ κ(G) has a hamiltonian cycle, where α(G) and κ(G) are the independence number and the connectivity of G, respectively. Oberly and Sumner [J. Graph Theory 3 (1979), 351–356] have proved that every connected, locally-connected claw-free graph of order at least three has a hamiltonian cycle. We study...
متن کاملThe Chvátal-Erdös condition for supereulerian graphs and the Hamiltonian index
A classical result of Chvátal and Erdős says that the graph G with connectivity κ(G) not less than its independent number α(G) (i.e. κ(G) ≥ α(G)) is hamiltonian. In this paper, we show that the graph G with κ(G) ≥ α(G) − 1 is either supereulerian, or the Petersen graph, or the graphs obtained from K2,3 by adding at most one vertex in one edge of K2,3 and by replacing exactly one vertex whose ne...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1985
ISSN: 0012-365X
DOI: 10.1016/0012-365x(85)90169-4