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

2009
*
Discrete Applied Mathematics
*

The independence

doi:10.1016/j.dam.2009.04.004
fatcat:lbp76dv2vraq7n7y64tm2iefim
*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. ...##
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On intersections of two-sided ideals of Leavitt path algebras
[article]

2015
*
arXiv
*
pre-print

Let E be an arbitrary directed

arXiv:1510.08871v1
fatcat:cqj5awzuhrbf5m6yldbvj3cdse
*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 ...##
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P-Matchings in Graphs: A Brief Survey with Some Open Problems
[article]

2018
*
arXiv
*
pre-print

For

arXiv:1805.03334v1
fatcat:kraqsc2fyfeuxake3hkyastwhi
*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. ...##
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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.” ...##
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A polynomial-time fragment of dominance constraints

2000
*
Proceedings of the 38th Annual Meeting on Association for Computational Linguistics - ACL '00
*

Here we identify the natural fragment

doi:10.3115/1075218.1075265
dblp:conf/acl/KollerMN00
fatcat:7eyra7l7szhuzih5jcp32qd7e4
*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. ...##
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Complete linear descriptions of small asymmetric traveling salesman polytopes

1995
*
Discrete Applied Mathematics
*

Using

doi:10.1016/0166-218x(95)98954-y
fatcat:daj3iu574raozbuzm54xqvitdy
*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. ...##
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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. ...##
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Packing triangles in low degree graphs and indifference graphs

2008
*
Discrete Mathematics
*

We consider the problems

doi:10.1016/j.disc.2007.07.100
fatcat:bjnkadauvrdmxfoyfc5ke6qcey
*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. ...##
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Author index

2002
*
Discrete Mathematics
*

Favaron, Independence,

doi:10.1016/s0012-365x(02)00738-0
fatcat:nspeq6c56za2hjedmozlhkc3r4
*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. ...##
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Reducing Weak to Strong Bisimilarity in CCP

2012
*
Electronic Proceedings in Theoretical Computer Science
*

However, only recently

doi:10.4204/eptcs.104.2
fatcat:a77s76fgffav5invsd43fgh2ca
*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. ...##
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Logical and algorithmic properties of stable conditional independence

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 ! ...

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

2021
*
arXiv
*
pre-print

We give necessary and sufficient conditions under which

arXiv:1911.01755v3
fatcat:bvxw5gpfrvha5lmyfkxljiqgqu
*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. . ...##
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The multiplicative ideal theory of Leavitt path algebras of directed graphs - a survey
[article]

2019
*
arXiv
*
pre-print

Let L be the Leavitt path algebra

arXiv:1902.00774v1
fatcat:s5ij6yee3rda5ebcmmoc4ylobe
*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). ...##
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Products and Intersections of Prime-Power Ideals in Leavitt Path Algebras
[article]

2021
*
arXiv
*
pre-print

We continue

arXiv:2101.05376v1
fatcat:qpblm2u4wrhnpct6h6ihwfkwue
*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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