scholarly journals Acyclic Subgraphs of Planar Digraphs

10.37236/4596 ◽  
2015 ◽  
Vol 22 (3) ◽  
Author(s):  
Noah Golowich ◽  
David Rolnick
Keyword(s):  
Directed Cycle ◽  
Acyclic Subgraph ◽  
Planar Digraph

An acyclic set in a digraph is a set of vertices that induces an acyclic subgraph. In 2011, Harutyunyan conjectured that every planar digraph on $n$ vertices without directed 2-cycles possesses an acyclic set of size at least $3n/5$. We prove this conjecture for digraphs where every directed cycle has length at least 8. More generally, if $g$ is the length of the shortest directed cycle, we show that there exists an acyclic set of size at least $(1 - 3/g)n$.

scholarly journals Linkedness and Ordered Cycles in Digraphs

2008 ◽  
Vol 17 (3) ◽  
pp. 411-422 ◽  
Author(s):  
DANIELA KÜHN ◽  
DERYK OSTHUS
Keyword(s):  
Directed Cycle

Given a digraphD, let δ0(D) := min{δ+(D), δ−(D)} be the minimum semi-degree ofD. We show that every sufficiently large digraphDwith δ0(D)≥n/2 +l−1 isl-linked. The bound on the minimum semi-degree is best possible and confirms a conjecture of Manoussakis [17]. We also determine the smallest minimum semi-degree which ensures that a sufficiently large digraphDisk-ordered,i.e., that for every sequences1, . . .,skof distinct vertices ofDthere is a directed cycle which encounterss1, . . .,skin this order. This result will be used in [16].

scholarly journals A directed cycle-based column-and-cut generation method for capacitated survivable network design

Networks ◽  
2004 ◽  
Vol 43 (4) ◽  
pp. 201-211 ◽  
Author(s):  
Deepak Rajan ◽  
Alper Atamtürk
Keyword(s):  
Network Design ◽  
Directed Cycle ◽  
Survivable Network Design ◽  
Survivable Network ◽  
Cut Generation

On the maximum acyclic subgraph problem under disjunctive constraints

2015 ◽  
Vol 115 (2) ◽  
pp. 119-124
Author(s):  
Sílvia Maria Santana Mapa ◽  
Sebastián Urrutia
Keyword(s):  
Disjunctive Constraints ◽  
Acyclic Subgraph

On the Advantage over Random for Maximum Acyclic Subgraph

2007 ◽  
Author(s):  
Moses Charikar ◽  
Konstantin Makarychev ◽  
Yury Maka
Keyword(s):  
Acyclic Subgraph

scholarly journals Balanced directed cycle designs based on cyclic groups

1995 ◽  
Vol 58 (2) ◽  
pp. 210-218 ◽  
Author(s):  
Chaufah Nilrat ◽  
Cheryl E. Praeger
Keyword(s):  
Directed Graph ◽  
Cyclic Group ◽  
Complete Classification ◽  
Directed Cycle ◽  
Group Of Automorphisms ◽  
Edge Disjoint ◽  
Cyclic Groups ◽  
Directed Cycles

AbstractA balanced directed cycle design with parameters (υ, k, 1), sometimes called a (υ, k, 1)-design, is a decomposition of the complete directed graph into edge disjoint directed cycles of length k. A complete classification is given of (υ, k, 1)-designs admitting the holomorph {øa, b: x ↦ ax + b∣ a, b ∈ Zυ, (a, υ1) = 1} of the cyclic group Zυ as a group of automorphisms. In particular it is shown that such a design exists if and ony if one of (a) k = 2, (b) p ≡ 1 (mod k) for each prime p dividing υ, or (c) k is the least prime dividing υ, k2 does not divide υ, and p ≡ 1 (mod k) for each prime p < k dividing υ.

scholarly journals The determinant of an antiadjacency matrix of a directed cycle graph with chords

2017 ◽  
Author(s):  
D. Diwyacitta ◽  
A. P. Putra ◽  
K. A. Sugeng ◽  
S. Utama
Keyword(s):  
Directed Cycle ◽  
Cycle Graph

scholarly journals Embedding partial bipartite directed cycle systems

2002 ◽  
Vol 244 (1-3) ◽  
pp. 269-278
Author(s):  
C.C. Lindner ◽  
Lorenzo Milazzo
Keyword(s):  
Directed Cycle ◽  
Cycle Systems

scholarly journals Balanced directed cycle designs based on groups

1991 ◽  
Vol 92 (1-3) ◽  
pp. 275-290 ◽  
Author(s):  
Cheryl E. Praeger
Keyword(s):  
Directed Cycle

scholarly journals Characterization of the Existence of anN0-Completion of a PartialN0-Matrix with an Associated Directed Cycle

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Cristina Jordán ◽  
Juan R. Torregrosa
Keyword(s):  
Matrix Completion ◽  
Directed Cycle ◽  
Partial Matrix

Ann×nmatrix is called anN0-matrix if all its specified principal minors are nonpositive. In the context of partial matrices, a partial matrix is called a partialN0-matrix if all its specified principal minors are nonpositive. In this paper we characterize the existence of anN0-matrix completion of a partialN0-matrix whose associated graph is a directed cycle.

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