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Packing triangles in regular tournaments
"... We prove that a regular tournament with n vertices has more than n 2 11.5 (1 − o(1)) pairwise arcdisjoint directed triangles. On the other hand, we construct regular tournaments with a feedback arc set of size less than n 2 8, so these tournaments do not have n2 8 pairwise arcdisjoint triangles. T ..."
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We prove that a regular tournament with n vertices has more than n 2 11.5 (1 − o(1)) pairwise arcdisjoint directed triangles. On the other hand, we construct regular tournaments with a feedback arc set of size less than n 2 8, so these tournaments do not have n2 8 pairwise arcdisjoint triangles
Routing Permutations and 21 Routing Requests in the Hypercube
, 2000
"... Let H n be the directed symmetric ndimensional hypercube. Using the computer, we show that for any permutation of the vertices of H 4 , there exists a system of pairwise arcdisjoint directed paths from each vertex to its target in the permutation. This veries Szymanski's conjecture [8] for n ..."
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Cited by 2 (0 self)
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Let H n be the directed symmetric ndimensional hypercube. Using the computer, we show that for any permutation of the vertices of H 4 , there exists a system of pairwise arcdisjoint directed paths from each vertex to its target in the permutation. This veries Szymanski's conjecture [8] for n
ArcDisjoint Paths in Expander Digraphs
 IN PROCEEDINGS OF THE 42ND ANNUAL IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE
, 2001
"... Given a digraph D = (V, A) and a set of n pairs of vertices in V, we axe interested in finding for each pair (xi, Yi), a directed path connecting xi to Yi, such that the set of n paths so found is axcdisjoint. For arbitrary graphs the problem is NPcomplete, even for n = 2. We present ..."
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Cited by 4 (0 self)
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Given a digraph D = (V, A) and a set of n pairs of vertices in V, we axe interested in finding for each pair (xi, Yi), a directed path connecting xi to Yi, such that the set of n paths so found is axcdisjoint. For arbitrary graphs the problem is NPcomplete, even for n = 2. We present
On a ⃗ C4ultrahomogeneous digraph
"... The notion of a Cultrahomogeneous graph, due to Isaksen et al., is adapted for digraphs, and subsequently a strongly connected ⃗ C4ultrahomogeneous digraph on 168 vertices and 126 pairwise arcdisjoint 4cycles is presented, with regular indegree and outdegree 3 and no circuits of lengths 2 and 3, ..."
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The notion of a Cultrahomogeneous graph, due to Isaksen et al., is adapted for digraphs, and subsequently a strongly connected ⃗ C4ultrahomogeneous digraph on 168 vertices and 126 pairwise arcdisjoint 4cycles is presented, with regular indegree and outdegree 3 and no circuits of lengths 2 and 3
On a ⃗ C4ultrahomogeneous oriented graph
"... The notion of a Cultrahomogeneous graph, due to Isaksen et al., is adapted for digraphs, and then a strongly connected ⃗ C4ultrahomogeneous oriented graph on 168 vertices and 126 pairwise arcdisjoint 4cycles is presented, with regular indegree and outdegree 3 and no circuits of lengths 2 and 3, ..."
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Cited by 3 (3 self)
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The notion of a Cultrahomogeneous graph, due to Isaksen et al., is adapted for digraphs, and then a strongly connected ⃗ C4ultrahomogeneous oriented graph on 168 vertices and 126 pairwise arcdisjoint 4cycles is presented, with regular indegree and outdegree 3 and no circuits of lengths 2 and 3
Wavelength Rerouting in Optical Networks, or the Venetian Routing Problem
 Journal of Algorithms
"... Wavelength rerouting has been suggested as a viable and costeffective method to improve the blocking performance of wavelengthrouted WavelengthDivision Multiplexing (WDM) networks. This method leads to the following combinatorial optimization problem, dubbed Venetian Routing. Given a directed mul ..."
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Cited by 1 (0 self)
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multigraph G along with two vertices s and t and a collection of pairwise arcdisjoint paths, we wish to find an stpath which arcintersects the smallest possible number of the given paths. In this paper we prove the computational hardness of this problem even in various special cases, and present several
Parameterized Directed kChinese Postman Problem and k ArcDisjoint Cycles Problem on Euler Digraphs
"... ar ..."
Routing Permutations in the Hypercube
, 1999
"... We study an ndimensional directed symmetric hypercube Hn , in which every pair of adjacent vertices is connected by two arcs of opposite directions. Using the computer, we show that for H4 and for any permutation on its vertices, there exists a system of pairwise arcdisjoint directed paths from ea ..."
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Cited by 1 (1 self)
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We study an ndimensional directed symmetric hypercube Hn , in which every pair of adjacent vertices is connected by two arcs of opposite directions. Using the computer, we show that for H4 and for any permutation on its vertices, there exists a system of pairwise arcdisjoint directed paths from
On Cultrahomogeneous graphs and digraphs
, 904
"... The notion of a Cultrahomogeneous graph, due to Isaksen et al., is adapted for digraphs and studied for the twelve cubic distance transitive graphs, with C formed by gcycles and (k − 1)paths, where g = girth and k = arctransitivity. Excluding the Petersen, Heawood and Foster (90 vertices) graphs ..."
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linegraphical Menger graph is K2fastened {K4, K2,2,2}ultrahomogeneous. Among other results, a strongly connected C4ultrahomogeneous digraph on 168 vertices and 126 pairwise arcdisjoint 4cycles is obtained, with regular indegree and outdegree 3 and no circuits of lengths 2 and 3, by altering a definition
Automated Consistency Checking of Requirements Specifications
, 1996
"... This paper describes a formal analysis technique, called consistency checking, for automatic detection of errors, such as type errors, nondeterminism, missing cases, and circular definitions, in requirements specifications. The technique is designed to analyze requirements specifications expressed i ..."
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Cited by 268 (33 self)
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This paper describes a formal analysis technique, called consistency checking, for automatic detection of errors, such as type errors, nondeterminism, missing cases, and circular definitions, in requirements specifications. The technique is designed to analyze requirements specifications expressed in the SCR (Software Cost Reduction) tabular notation. As background, the SCR approach to specifying requirements is reviewed. To provide a formal semantics for the SCR notation and a foundation for consistency checking, a formal requirements model is introduced; the model represents a software system as a finite state automaton, which produces externally visible outputs in response to changes in monitored environmental quantities. Results are presented of two experiments which evaluated the utility and sealability of our technique for consistency checking in a realworld avionics application. The role of consistency checking during the requirements phase of software development is discussed.
Results 1  10
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12,301