Cycles and paths in semicomplete multipartite digraphs, theorems, and algorithms: a survey
نویسنده
چکیده
A digraph obtained by replacing each edge of a complete m-partite graph by an arc or a pair of mutually opposite arcs with the same end vertices is called a semicomplete m-partite digraph. We describe results (theorems and algorithms) on directed walks in semicomplete mpartite digraphs including some recent results concerning tournaments.
منابع مشابه
Paths and cycles in extended and decomposable digraphs,
We consider digraphs – called extended locally semicomplete digraphs, or extended LSD’s, for short – that can be obtained from locally semicomplete digraphs by substituting independent sets for vertices. We characterize Hamiltonian extended LSD’s as well as extended LSD’s containing Hamiltonian paths. These results as well as some additional ones imply polynomial algorithms for finding a longes...
متن کاملA Polynomial Time Algorithm for Finding a Cycle Covering a Given Set of Vertices in a Semicomplete Multipartite Digraph
The existens of a polynomial algorithm for nding a cycle covering a given set of vertices in a semicomplete multipartite digraph (if it exists) was conjectured by Bang-Jensen, Gutin and Yeo in 4]. The analog problem for semicomplete bipartite digraphs was conjectured by Bang-Jensen and Manoussakis in 5]. We prove the conjecture from 4] in the aarmative, which also implies the conjecture from 5]...
متن کاملSolution of a Conjecture of Volkmann on the Number of Vertices in Longest Paths and Cycles of Strong Semicomplete Multipartite Digraphs
A digraph obtained by replacing each edge of a complete multipartite graph by an arc or a pair of mutually opposite arcs with the same end vertices is called a semicomplete multipartite digraph. L. Volkmann conjectured that l ≤ 2c− 1, where l (c, respectively) is the number of vertices in a longest path (longest cycle) of a strong semicomplete multipartite digraph. The bound on l is sharp. We s...
متن کاملStrongly connected spanning subgraphs with the minimum number of arcs in semicomplete multipartite digraphs
We consider the problem (MSSS) of finding the minimum number of arcs in a spanning strongly connected subgraph of a strongly connected digraph. This problem is NP-hard for general digraphs since it generalizes the hamiltonian cycle problem. We characterize the number of arcs in a minimum spanning strong subgraph for digraphs which are either extended semicomplete or semicomplete bipartite. Our ...
متن کاملLocal Tournaments and In - Tournaments
Preface Tournaments constitute perhaps the most well-studied class of directed graphs. One of the reasons for the interest in the theory of tournaments is the monograph Topics on Tournaments [58] by Moon published in 1968, covering all results on tournaments known up to this time. In particular, three results deserve special mention: in 1934 Rédei [60] proved that every tournament has a directe...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Journal of Graph Theory
دوره 19 شماره
صفحات -
تاریخ انتشار 1995