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### Page 6820 of Mathematical Reviews Vol. , Issue 2000j [page]

2000 Mathematical Reviews
sharp edge bound on the interval number of a graph.  ...  As the main result we prove that, for any finite family ¥, the minimum number of edges of an ¥-saturated hypergraph is O(n*~!). In particular, this implies a conjecture of Tuza.  ...

### Variable neighborhood search for extremal graphs. 22. Extending bounds for independence to upper irredundance

Mustapha Aouchiche, Odile Favaron, Pierre Hansen
2009 Discrete Applied Mathematics
The independence number α (resp. upper irredundance number IR) is the maximum number of vertices of an independent (resp. irredundant) set of G.  ...  A set of vertices U in a graph G is irredundant if each vertex v of U has a private neighbor, which may be v itself, i.e., a neighbor of v which is not a neighbor of any other vertex of U.  ...  Acknowledgements This work was done in part during a visit of the second author to GERAD, Montreal in April 2006.  ...

### On intersections of two-sided ideals of Leavitt path algebras [article]

Songül Esin, Müge Kanuni, K.M. Rangaswamy
2015 arXiv   pre-print
Let E be an arbitrary directed graph and let L be the Leavitt path algebra of the graph E over a field K.  ...  Uniqueness theorems in representing an ideal of L as an irredundant intersection and also as an irredundant product of finitely many prime ideals are established.  ...  Acknowledgement: We thank Professor Astrid an Huef for raising the question of intersections of primitive ideals in a Leavitt path algebra and Professor Pere Ara for helpful preliminary discussion on this  ...

### P-Matchings in Graphs: A Brief Survey with Some Open Problems [article]

Todd Fenstermacher, Soumendra Ganguly, Stephen Hedetniemi, Renu Laskar
2018 arXiv   pre-print
For a graph G=(V,E), a matching M is a set of independent edges. The topic of matchings is well studied in graph theory. In this paper many varieties of matchings are discussed.  ...  A matching M is perfect if it saturates all the vertices of G.  ...  The lower matching number of G is β − 1 (G) = min{ M ∶ M is a maximal matching}. The matching number and lower matching number are demonstrated in Figure 1.  ...

### Page 7334 of Mathematical Reviews Vol. , Issue 97M [page]

1997 Mathematical Reviews
The authors give a recursive procedure for finding the number of maximum independent sets in a functional graph.  ...  For each order n > 3, the number of primitive minimally triangle- saturated graphs of order n yielded by the relevant construction is exponentially quadratic in n.”  ...

### A polynomial-time fragment of dominance constraints

Alexander Koller, Kurt Mehlhorn, Joachim Niehren
2000 Proceedings of the 38th Annual Meeting on Association for Computational Linguistics - ACL '00
Here we identify the natural fragment of normal dominance constraints and show that its satisfiability problem is in deterministic polynomial time.  ...  Dominance constraints are logical descriptions of trees that are widely used in computational linguistics. Their general satisfiability problem is known to be NP-complete.  ...  We would like to thank Ernst Althaus, Denys Duchier, Gert Smolka, Sven Thiel, all members of the SFB 378 project CHORUS at the University of the Saarland, and our reviewers.  ...

### Complete linear descriptions of small asymmetric traveling salesman polytopes

R. Euler, H. Le Verge
1995 Discrete Applied Mathematics
Using a refined version of Chernikova's algorithm we determined a complete and irredundant linear description of small asymmetric traveling salesman polytopes.  ...  We present such a description for the monotone polytope on 5 nodes consisting of 7615 facet-defining inequalities, and we present 319 015 facet-defining inequalities which, together with 11 equations,  ...  valid inequality must saturate a larger set of vertices.  ...

### Page 06 of Mathematical Reviews Vol. , Issue 90I [page]

1990 Mathematical Reviews
The main results of this paper are the inequalities OIR(G) < r(G) if G has no isolates and IR(G) < r(N(G)), where IR(G) and OIR(G) denote the upper irredundance number and open upper irredundance number  ...  The binding number of a graph G = (V, E) is defined by |N(X)| bind(G) = redler xT” where X C V, and N(X) denotes the set of neighbours of YX.  ...

### Packing triangles in low degree graphs and indifference graphs

Gordana Manić, Yoshiko Wakabayashi
2008 Discrete Mathematics
We consider the problems of finding the maximum number of vertex-disjoint triangles (VTP) and edge-disjoint triangles (ETP) in a simple graph. Both problems are NP-hard.  ...  We also present an exact linear-time algorithm for VTP on the class of indifference graphs.  ...  Acknowledgements We thank the referees for the suggestions and remarks that improved the presentation of this paper.  ...

### Author index

2002 Discrete Mathematics
Favaron, Independence, irredundance, degrees and chromatic number in graphs (Note) , J.A., Thresholds for random distributions on graph sequences with applications to pebbling (1-3) 59-69 Bryant, D.E.  ...  Mauro, On generalized Petersen graphs labeled with a condition at distance two (Note) (1-3) 311-318 Horton, J.D. and W.D. Wallis, Factoring the cartesian product of a cubic graph and , Y., see R.  ...

### Reducing Weak to Strong Bisimilarity in CCP

Andrés Aristizábal, Filippo Bonchi, Luis Pino, Frank Valencia
2012 Electronic Proceedings in Theoretical Computer Science
However, only recently a well-behaved notion of bisimilarity for ccp, and a ccp partition refinement algorithm for deciding the strong version of this equivalence have been proposed.  ...  In this paper we demonstrate that, because of its involved labeled transitions, the above-mentioned saturation technique does not work for ccp.  ...  We then presented a new transition relation using another saturation mechanism and showed that it is complete for ccp.  ...

### Logical and algorithmic properties of stable conditional independence

Mathias Niepert, Dirk Van Gucht, Marc Gyssens
2010 International Journal of Approximate Reasoning
A special case for which the stability of the CI statement IðA; BjCÞ is guaranteed is the situation where BjCÞ is said to be saturated.)  ...  Technically, the notion of stability of a CI statement IðA; BjCÞ, in the context of a set of random variables S and a set of CI statements C, is defined by requiring that, for every superset C 0 C which  ...  Fig. 4 . 4 Size of irredundant equivalent subset of a set of initially 500 stable CI statements for different numbers of attributes. IðA; ;jCÞ Triviality IðA; BjCÞ !  ...

### Variations of primeness and Factorization of ideals in Leavitt Path Algebras [article]

Sarah Aljojani, Katherin Radler, K. M. Rangaswamy, Ashish K. Srivastava
2021 arXiv   pre-print
We give necessary and sufficient conditions under which a proper ideal of a Leavitt path algebra L is a product as well as an intersection of finitely many of these different types of prime ideals.  ...  Such factorizations, when they are irredundant, are shown to be unique except for the order of the factors.  ...  every admissible pair (H, S), (E\(H, S)) 0 is the union of a finite number of maximal tails. .  ...

### The multiplicative ideal theory of Leavitt path algebras of directed graphs - a survey [article]

Kulumani M Rangaswamy
2019 arXiv   pre-print
Let L be the Leavitt path algebra of an arbitrary directed graph E over a field K.  ...  This survey article describes how this highly non-commutative ring L shares a number of the characterizing properties of a Dedekind domain or a Pr\"ufer domain expressed in terms of their ideal lattices  ...  the number of distinct prime ideals in an irredundant factorization of gr(I).  ...

### Products and Intersections of Prime-Power Ideals in Leavitt Path Algebras [article]

Zachary Mesyan, Kulumani M. Rangaswamy
2021 arXiv   pre-print
We continue a very fruitful line of inquiry into the multiplicative ideal theory of an arbitrary Leavitt path algebra L.  ...  Specifically, we show that factorizations of an ideal in L into irredundant products or intersections of finitely many prime-power ideals are unique, provided that the ideals involved are powers of distinct  ...  Acknowledgement We are grateful to the referee for a careful reading of the manuscript.  ...
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