Partition of a directed bipartite graph into two directed cycles
نویسندگان
چکیده
منابع مشابه
Vertex disjoint cycles in a directed graph
Let D be a directed graph of order n 4 and minimum degree at least (3n 3)/2. Let n = nI + n2 where nl 2 and n2 2. Then D contains two vertex-disjoint directed cycles of nI and n2 respectively. The result is sharp if n ~ 6: we give counterexamples if the condition on the minimum degree is relaxed. 1 Introduction We discuss only finite simple graphs and strict and use standard terminology and not...
متن کاملDirected prime graph of non-commutative ring
Prime graph of a ring R is a graph whose vertex set is the whole set R any any two elements $x$ and $y$ of $R$ are adjacent in the graph if and only if $xRy = 0$ or $yRx = 0$. Prime graph of a ring is denoted by $PG(R)$. Directed prime graphs for non-commutative rings and connectivity in the graph are studied in the present paper. The diameter and girth of this graph are also studied in the pa...
متن کاملPartition of a graph into cycles and isolated vertices
Let k, r, n be integers with k ≥ 2, 0 ≤ r ≤ k−1 and n ≥ 10k+3. We prove that if G is a graph of order n such that the degree sum of any pair of nonadjacent vertices is at least n−r, then G contains k vertexdisjoint subgraphs Hi, 1 ≤ i ≤ k, such that V (H1) ∪ . . . ∪ V (Hk) = V (G) and such that Hi is a cycle or isomorphic to K1 for each i with 1 ≤ i ≤ r, and Hi is a cycle for each i with r + 1 ...
متن کاملPacking Directed Cycles Efficiently
Let G be a simple digraph. The dicycle packing number of G, denoted νc(G), is the maximum size of a set of arc-disjoint directed cycles in G. Let G be a digraph with a nonnegative arcweight function w. A function ψ from the set C of directed cycles in G to R+ is a fractional dicycle packing of G if ∑ e∈C∈C ψ(C) ≤ w(e) for each e ∈ E(G). The fractional dicycle packing number, denoted ν c (G,w), ...
متن کاملColoring directed cycles
Sopena in his survey [E. Sopena, The oriented chromatic number of graphs: A short survey, preprint 2013] writes, without any proof, that an oriented cycle ~ C can be colored with three colors if and only if λ( ~ C) = 0, where λ( ~ C) is the number of forward arcs minus the number of backward arcs in ~ C. This is not true. In this paper we show that ~ C can be colored with three colors if and on...
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: 1996
ISSN: 0012-365X
DOI: 10.1016/0012-365x(95)00165-s