Results 1 to 10 of about 20,394 (53)
Blocking optimal $k$-arborescences [PDF]
, 2007 Given a digraph $D=(V,A)$ and a positive integer $k$, an arc set $F\subseteq A$ is called a \textbf{$k$-arborescence} if it is the disjoint union of $k$ spanning arborescences.
Bernáth, Attila, Király, Tamás
core +4 more sources
Kernels for Feedback Arc Set In Tournaments [PDF]
, 2009 A tournament T=(V,A) is a directed graph in which there is exactly one arc between every pair of distinct vertices. Given a digraph on n vertices and an integer parameter k, the Feedback Arc Set problem asks whether the given digraph has a set of k arcs ...
Bessy, Stéphane +6 more
core +9 more sources
Beyond Bidimensionality: Parameterized Subexponential Algorithms on Directed Graphs [PDF]
, 2010 We develop two different methods to achieve subexponential time parameterized algorithms for problems on sparse directed graphs. We exemplify our approaches with two well studied problems.
Dorn, Frederic +4 more
core +5 more sources
Universal and Near-Universal Cycles of Set Partitions [PDF]
, 2015 We study universal cycles of the set ${\cal P}(n,k)$ of $k$-partitions of the set $[n]:=\{1,2,\ldots,n\}$ and prove that the transition digraph associated with ${\cal P}(n,k)$ is Eulerian. But this does not imply that universal cycles (or ucycles) exist,
Godbole, Anant +3 more
core +1 more source
Out-degree reducing partitions of digraphs [PDF]
, 2017 Let $k$ be a fixed integer. We determine the complexity of finding a $p$-partition $(V_1, \dots, V_p)$ of the vertex set of a given digraph such that the maximum out-degree of each of the digraphs induced by $V_i$, ($1\leq i\leq p$) is at least $k ...
Bang-Jensen, Joergen +3 more
core +5 more sources
Finding Even Subgraphs Even Faster [PDF]
, 2014 Problems of the following kind have been the focus of much recent research in the realm of parameterized complexity: Given an input graph (digraph) on $n$ vertices and a positive integer parameter $k$, find if there exist $k$ edges (arcs) whose deletion ...
Goyal, Prachi +4 more
core +4 more sources
New Bounds for the Dichromatic Number of a Digraph
, 2019 The chromatic number of a graph $G$, denoted by $\chi(G)$, is the minimum $k$ such that $G$ admits a $k$-coloring of its vertex set in such a way that each color class is an independent set (a set of pairwise non-adjacent vertices).
Cordero-Michel, Narda +1 more
core +1 more source
On (4,2)-digraph Containing a Cycle of Length 2 [PDF]
, 2000 A diregular digraph is a digraph with the in-degree and out-degree of all vertices is constant. The Moore bound for a diregular digraph of degree d and diameter k is M_{d,k}=l+d+d^2+...+d^k.
Baskoro, Edy Tri, Iswadi, Hazrul
core
The maximal spectral radius of a digraph with (m+1)^2 - s edges
, 2003 It is known that the spectral radius of a digraph with k edges is \le \sqrt{k}, and that this inequality is strict except when k is a perfect square. For k=m^2 + \ell, \ell fixed, m large, Friedland showed that the optimal digraph is obtained from the ...
Snellman, Jan
core +1 more source
Efficient, Optimal $k$-Leader Selection for Coherent, One-Dimensional Formations
, 2014 We study the problem of optimal leader selection in consensus networks with noisy relative information. The objective is to identify the set of $k$ leaders that minimizes the formation's deviation from the desired trajectory established by the leaders ...
Dyagilev, Kirill +2 more
core +1 more source