Concentric subgraphs, closed subsets and dense graphs

1984 ◽  
pp. 100-118 ◽  
Author(s):  
K. M. Koh ◽  
N. Sauer
Keyword(s):  
Dense Graphs

Cycle factors in dense graphs

1999 ◽  
Vol 197-198 (1-3) ◽  
pp. 309-323 ◽  
Author(s):  
E Fischer
Keyword(s):  
Dense Graphs

Mixed Ramsey Numbers Revisited

2003 ◽  
Vol 12 (5-6) ◽  
pp. 653-660
Author(s):  
C. C. Rousseau ◽  
S. E. Speed
Keyword(s):  
Asymptotic Behaviour ◽  
Ramsey Number ◽  
Open Problems ◽  
Free Graph ◽  
Ramsey Numbers ◽  
Dense Graphs

Given a graph Hwith no isolates, the (generalized) mixed Ramsey number is the smallest integer r such that every H-free graph of order r contains an m-element irredundant set. We consider some questions concerning the asymptotic behaviour of this number (i) with H fixed and , (ii) with m fixed and a sequence of dense graphs, in particular for the sequence . Open problems are mentioned throughout the paper.

On the Benefits of Adaptivity in Property Testing of Dense Graphs

Algorithmica ◽  
2008 ◽  
Vol 58 (4) ◽  
pp. 811-830 ◽  
Author(s):  
Mira Gonen ◽  
Dana Ron
Keyword(s):  
Property Testing ◽  
Dense Graphs

scholarly journals Colouring and Covering Nowhere Dense Graphs

2016 ◽  
pp. 325-338 ◽  
Author(s):  
Martin Grohe ◽  
Stephan Kreutzer ◽  
Roman Rabinovich ◽  
Sebastian Siebertz ◽  
Konstantinos Stavropoulos
Keyword(s):  
Dense Graphs

scholarly journals A Note on Color-Bias Hamilton Cycles in Dense Graphs

2021 ◽  
Vol 35 (2) ◽  
pp. 970-975
Author(s):  
Andrea Freschi ◽  
Joseph Hyde ◽  
Joanna Lada ◽  
Andrew Treglown
Keyword(s):  
Hamilton Cycles ◽  
Dense Graphs ◽  
Color Bias

scholarly journals How Many Pairwise Preferences Do We Need to Rank a Graph Consistently?

2019 ◽  
Vol 33 ◽  
pp. 4830-4837
Author(s):  
Aadirupa Saha ◽  
Rakesh Shivanna ◽  
Chiranjib Bhattacharyya
Keyword(s):  
Optimal Recovery ◽  
Learning Problems ◽  
Sample Complexity ◽  
Strong Product ◽  
Large N ◽  
Dense Graphs ◽  
Node Connectivity ◽  
Real World Datasets ◽  
Statistical Consistency ◽  
First Time

We consider the problem of optimal recovery of true ranking of n items from a randomly chosen subset of their pairwise preferences. It is well known that without any further assumption, one requires a sample size of Ω(n2) for the purpose. We analyze the problem with an additional structure of relational graph G([n],E) over the n items added with an assumption of locality: Neighboring items are similar in their rankings. Noting the preferential nature of the data, we choose to embed not the graph, but, its strong product to capture the pairwise node relationships. Furthermore, unlike existing literature that uses Laplacian embedding for graph based learning problems, we use a richer class of graph embeddings—orthonormal representations—that includes (normalized) Laplacian as its special case. Our proposed algorithm, Pref-Rank, predicts the underlying ranking using an SVM based approach using the chosen embedding of the product graph, and is the first to provide statistical consistency on two ranking losses: Kendall’s tau and Spearman’s footrule, with a required sample complexity of O(n2χ(G¯))⅔ pairs, χ(G¯) being the chromatic number of the complement graph G¯. Clearly, our sample complexity is smaller for dense graphs, with χ(G¯) characterizing the degree of node connectivity, which is also intuitive due to the locality assumption e.g. O(n4/3) for union of k-cliques, or O(n5/3) for random and power law graphs etc.—a quantity much smaller than the fundamental limit of Ω(n2) for large n. This, for the first time, relates ranking complexity to structural properties of the graph. We also report experimental evaluations on different synthetic and real-world datasets, where our algorithm is shown to outperform the state of the art methods.

scholarly journals Approximating edge dominating set in dense graphs

2012 ◽  
Vol 414 (1) ◽  
pp. 92-99 ◽  
Author(s):  
Richard Schmied ◽  
Claus Viehmann
Keyword(s):  
Dominating Set ◽  
Edge Dominating Set ◽  
Dense Graphs
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