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Graph Cores via Universal Completability

Chris Godsil, David Roberson, Brendan Rooney, Robert Šámal, Antonios Varvitsiotis
2015 Electronic Notes in Discrete Mathematics  
In this work we identify a new sufficient condition for showing that a graph is a core in terms of the universal completability of an appropriate framework for the graph.  ...  To use this condition we develop a method for constructing universally completable frameworks based on the eigenvectors for the smallest eigenspace of the graph.  ...  This work builds on the following theorem which establishes an unexpected relationship between universal completability and graph cores.  ... 
doi:10.1016/j.endm.2015.06.046 fatcat:dbksufyb3zh3bazatzwiz22vlm

Compact Metrizable Structures via Projective Fraïssé Theory With an Application to the Study of Fences

Gianluca Basso
2020 Bulletin of Symbolic Logic  
An orbit equivalence relation E is called complete (or universal) if all orbit equivalence relations are Borel reducible to E.  ...  They asked whether the homeomorphism at https://www.cambridge.org/core/terms. https://doi.  ...  Preprint arXiv:2001.05338 of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/bsl.2020.38 Downloaded from https://www.cambridge.org/core.  ... 
doi:10.1017/bsl.2020.38 fatcat:sotqkoztnvbrtbzii7ozblqa3u

QUASI RIESZ TRANSFORMS, HARDY SPACES AND GENERALISED SUB-GAUSSIAN HEAT KERNEL ESTIMATES

LI CHEN
2015 Bulletin of the Australian Mathematical Society  
Then we show that the two H 1 spaces via molecules and via square functions are the same. Also, we compare the H p space defined via square functions with L p .  ...  In Chapter 1, we consider an arbitrary complete noncompact Riemannian manifold without any volume or heat kernel estimate assumptions.  ... 
doi:10.1017/s0004972715000714 fatcat:m53zg74fovglzd5np4resm2bgu

Characterization and recognition of generalized clique-Helly graphs

Mitre C. Dourado, Fábio Protti, Jayme L. Szwarcfiter
2007 Discrete Applied Mathematics  
A graph G is a (p, q)-clique-Helly graph when its family of (maximal) cliques is (p, q)-Helly.  ...  According to this terminology, the usual Helly property and the clique-Helly graphs correspond to the case p = 2, q = 1. In this work we present a characterization for (p, q)-clique-Helly graphs.  ...  Since F is (1, q)-intersecting by hypothesis, it has q + -core. This means that G c [F] contains (at least) q universal vertices. Hence, G[W ] contains q universal vertices.  ... 
doi:10.1016/j.dam.2007.06.013 fatcat:krithlej2jd3zfdh3yzse6hvjm

CORE: A Knowledge Graph Entity Type Prediction Method via Complex Space Regression and Embedding [article]

Xiou Ge, Yun-Cheng Wang, Bin Wang, C.-C. Jay Kuo
2021 arXiv   pre-print
Entity type prediction is an important problem in knowledge graph (KG) research. A new KG entity type prediction method, named CORE (COmplex space Regression and Embedding), is proposed in this work.  ...  The proposed CORE method leverages the expressive power of two complex space embedding models; namely, RotatE and ComplEx models.  ...  CORE: A Knowledge Graph Entity Type Prediction Method via Complex Space Regression and Embedding Figure 1: A KG with the entity type information.  ... 
arXiv:2112.10067v1 fatcat:7ehs7mqagbcgxcaq5jilnsdkcq

Page 5375 of Mathematical Reviews Vol. , Issue 90I [page]

1990 Mathematical Reviews  
As a result, they obtain as a corollary that if P # NP then nonsparse re- cursive proper cores exist for all NP-complete and co-NP-complete sets, and that a particular NP-complete set has such a core if  ...  The main results include the fact that if P # NP then every weakly paddable NP-complete or co-NP-complete set has a nonsparse proper complexity core in DEXT.  ... 

A family of universal pseudo-homogeneous G-colourable graphs

Anthony Bonato
2002 Discrete Mathematics  
For each ÿnite core graph G there is a countable universal pseudo-homogeneous G-colourable graph M (G) that is unique up to isomorphism.  ...  We also investigate limits of the graphs M (Gi), and we answer a question of Caicedo (Algebra Universalis 34 (1995) 314) on inÿnite antichains in the lattice of cores.  ...  Each of the complete graphs and odd cycles are cores, as is the Petersen graph. A graph has a homomorphism into K n if and only if it is n-colourable.  ... 
doi:10.1016/s0012-365x(01)00158-3 fatcat:hloza76khrdfplw4z44y4jv3hi

Constraint Satisfaction Problems for Reducts of Homogeneous Graphs

Manuel Bodirsky, Barnaby Martin, Michael Pinsker, András Pongrácz
2019 SIAM journal on computing (Print)  
universal for the class of finite graphs.  ...  homogeneous graphs: all such problems are either in P or NP-complete.  ...  Similarly to the case of the Henson graphs, we start with unary polymorphisms in Section 6.1, reducing the problem to model-complete cores.  ... 
doi:10.1137/16m1082974 fatcat:piol3ztb7ffjde4tkpewjxxfze

Deliverable 4.3 Using Advanced PIDGraph Functionality inPilot Applications - revised

Tina Dohna, Ketil Koop-Jakobsen, Uwe Schindler, Artemis Lavasa, Pamfilos Fokianos, Sünje Dallmeier-Tiessen, Vasily Bunakov, Frances Madden, Christine Ferguson
2019 Zenodo  
of application of the PID Graph idea.  ...  This deliverable of the FREYA project describes the work carried out on integrating PID Graph functionality in the disciplinary contexts of FREYA consortium partner systems, demonstrating the diversity  ...  Users of the Bremen Core Repository can get sediment core sections or samples from a core delivered for their research, either in a laboratory at Bremen University or in their own laboratory upon request  ... 
doi:10.5281/zenodo.4292126 fatcat:iu5lnl2k6vhxjceldgst4fpvzu

QRE volume 19 issue 1 Cover and Back matter

2012 Queensland Review  
She completed the Masters course at the Institute of Advanced Architectural Studies at the University of York in England in 1990, and was awarded her PhD in 2000.  ...  Kyleigh Simpson is a children's author who has recently completed postgraduate studies in early learning.  ... 
doi:10.1017/qre.2012.17 fatcat:o4yz6cy4b5aitgszuiafr6gwwy

On the strong p-Helly property

Mitre C. Dourado, Fábio Protti, Jayme L. Szwarcfiter
2008 Discrete Applied Mathematics  
In contrast, we show that the recognition problem is co-NP-complete, for arbitrary p.  ...  Further, we apply the concept of strong p-Helly hypergraphs to the cliques of a graph, leading to the class of strong p-clique-Helly graphs.  ...  A vertex is universal if it is adjacent to any other vertex of the graph. Theorem 3 (Dourado et al. [4]).  ... 
doi:10.1016/j.dam.2007.05.047 fatcat:ly2qavmkpjclfhb6jki5hi3zda

Data exchange

Ronald Fagin, Phokion G. Kolaitis, Lucian Popa
2003 Proceedings of the twenty-second ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems - PODS '03  
We also analyze the computational complexity of the following decision problem that underlies the computation of cores: given two graphs G and H, is H the core of G?  ...  All universal solutions have the same core (up to isomorphism); we show that this core is also a universal solution, and hence the smallest universal solution.  ...  Can We Obtain the Core Via the Chase? A universal solution can be obtained via the chase [Fagin et al. 2003 ]. What about the core?  ... 
doi:10.1145/773153.773163 dblp:conf/pods/FaginKP03 fatcat:pygtrcoiojf63nknc6ainn23my

Data exchange: getting to the core

Ronald Fagin, Phokion G. Kolaitis, Lucian Popa
2005 ACM Transactions on Database Systems  
We also analyze the computational complexity of the following decision problem that underlies the computation of cores: given two graphs G and H, is H the core of G?  ...  All universal solutions have the same core (up to isomorphism); we show that this core is also a universal solution, and hence the smallest universal solution.  ...  Can We Obtain the Core Via the Chase? A universal solution can be obtained via the chase [Fagin et al. 2003 ]. What about the core?  ... 
doi:10.1145/1061318.1061323 fatcat:usqqjntxzvddzipuwcxgnzbhve

Towards Narrative Information Systems [chapter]

Philipp Wille, Christoph Lofi, Wolf-Tilo Balke
2015 Lecture Notes in Computer Science  
We show how to construct query-dependent plot graphs from unstructured data sources.  ...  While the shown plot graph looks similar to knowledge graphs as for example in [2, 3] , the core difference is that the shown plot graph can be transformed into a textual representation (story) via story  ...  Given a universe graph, a user can search its collection by issuing a query featuring a topic 𝑇 𝐶 .  ... 
doi:10.1007/978-3-319-21042-1_52 fatcat:zvzecavflvfrvglztnxapyspuy

Network Robustness via Global k-cores [article]

Palash Dey, Suman Kalyan Maity, Sourav Medya, Arlei Silva
2020 arXiv   pre-print
Therefore, previous work has attempted to model network robustness via the stability of its k-core.  ...  Our goal is to compute robustness via a combinatorial problem: find b most critical nodes to delete such that the number of nodes that fall from their initial cores is maximized.  ...  This follows from the observation that the Set Cover problem remains NP-complete even if the size of each subset is 3 and every element of the universe belongs to exactly 2 subsets [9] .  ... 
arXiv:2012.10036v1 fatcat:vxu5fencpzb3hgftghot2xbcda
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