Results 31 to 40 of about 105 (77)
Extremal results on feedback arc sets in digraphs
Random Structures &Algorithms, Volume 64, Issue 2, Page 287-308, March 2024.Abstract For an oriented graph G$$ G $$, let β(G)$$ \beta (G) $$ denote the size of a minimum feedback arc set, a smallest edge subset whose deletion leaves an acyclic subgraph. Berger and Shor proved that any m$$ m $$‐edge oriented graph G$$ G $$ satisfies β(G)=m/2−Ω(m3/4)$$ \beta (G)=m/2-\Omega \left({m}^{3/4}\right) $$.
Jacob Fox, Zoe Himwich, Nitya Mani
wiley +1 more source
Paths, cycles and related partitioning problems in graphs [PDF]
, 2017 In this thesis we contribute with new theoretical results and algorithms to the research area related to cycles and paths in (directed) graphs. In Chapter 2, we improve a classical result of Woodall for Hamiltonicity in digraphs, involving the sum of the
Zhang, Zanbo
core +1 more source
Preserving Regular Tournaments and Term Rank-1
, 2009 We investigate linear operators which map certain types of tournaments to themselves. To this end we also characterize term rank-1 preservers on the set of matrices whose associated digraphs are simple loopless directed graphs, and find that this set of ...
Guterman, Alexander E. +2 more
core +1 more source
A well-quasi-order for tournaments
, 2011 A digraph H is immersed in a digraph G if the vertices of H are mapped to (distinct) vertices of G, and the edges of H are mapped to directed paths joining the corresponding pairs of vertices of G, in such a way that the paths are pairwise edge-disjoint.
Paul Seymour +3 more
core +1 more source
Hall exponents of matrices, tournaments and their line digraphs [PDF]
, 2011 summary:Let $A$ be a square $(0,1)$-matrix. Then $A$ is a Hall matrix provided it has a nonzero permanent. The Hall exponent of $A$ is the smallest positive integer $k$, if such exists, such that $A^k$ is a Hall matrix.
Brualdi, Richard A. +1 more
core +1 more source
The outflow ranking method for weighted directed graphs
, 2009 A ranking method assigns to every weighted directed graph a (weak) ordering of the nodes. In this paper we axiomatize the ranking method that ranks the nodes according to their outflow using four independent axioms.
Gilles, R.P. +5 more
core +1 more source
New Algorithms and Lower Bounds for Streaming Tournaments [PDF]
We study fundamental directed graph (digraph) problems in the streaming model. An initial investigation by Chakrabarti, Ghosh, McGregor, and Vorotnikova [SODA'20] on streaming digraphs showed that while most of these problems are provably hard in general,
Kuchlous, Sahil, Ghosh, Prantar
core +1 more source
Irregularity Strength of Digraphs
, 2008 It is an elementary exercise to show that any non-trivial simple graph has two vertices with the same degree. This is not the case for digraphs and multigraphs. We consider generating irregular digraphs from arbitrary digraphs by adding multiple arcs. To
Michael Jacobson +7 more
core +1 more source
Generalizations of tournaments: A survey
, 1996 We survey results concerning various generalizations of tournaments. The reader will see that tournaments are by no means the only class of directed graphs with a very rich structure.
Gregory Gutin, Jørgen Bang-Jensen
core
On Containment Relations in Directed Graphs
, 2013 Containment relations in graphs such as induced subgraphs, minors, or immersions can be naturally extended to the world of directed graphs. In this thesis, we present new results on several containment relations in digraphs. The first
Kim, Ilhee
core