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Definability and Complexity of Graph Parameters
"... In this talk we survey definability and complexity results of graph parameters which take values in some ring or field R. ..."
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In this talk we survey definability and complexity results of graph parameters which take values in some ring or field R.
The graph parameter hierarchy
, 2013
"... The purpose of this document is to gather graph parameters (also called graph invariants) and their relationships in a central place. It was edited by Manuel Sorge 1 and Mathias Weller 2 with contributions by Ondˇrej Such´y, and Gerhard J. Woeginger. This project and the diagram shown in Figure 1 is ..."
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Cited by 1 (0 self)
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The purpose of this document is to gather graph parameters (also called graph invariants) and their relationships in a central place. It was edited by Manuel Sorge 1 and Mathias Weller 2 with contributions by Ondˇrej Such´y, and Gerhard J. Woeginger. This project and the diagram shown in Figure 1
ON THE CONTINUITY OF GRAPH PARAMETERS
"... Abstract. In this paper, we explore the mathematical properties of a distance function between graphs based on the maximum size of a common subgraph. The notion of distance between graphs has proven useful in many areas involving graph based structures such as chemistry, biology and pattern recognit ..."
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-Renyi probability space G(n, p) almost always is near the maximum attainable value. Finally, we define a notion of continuity of graph parameters and relate it to a property of graphs that can be easily verified. We also determine whether the normalized versions of some common graph parameters are continous
Connection matrices and the definability of graph parameters
- In CSL
, 2009
"... In this paper we extend the Finite Rank Theorem for connection matrices of graph parameters definable in Monadic Second Order Logic with modular counting CMSOL of B. Godlin, T. Kotek and J.A. Makowsky, [16, 30], and demonstrate its vast applicability in simplifying known and new non-definability res ..."
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Cited by 4 (3 self)
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In this paper we extend the Finite Rank Theorem for connection matrices of graph parameters definable in Monadic Second Order Logic with modular counting CMSOL of B. Godlin, T. Kotek and J.A. Makowsky, [16, 30], and demonstrate its vast applicability in simplifying known and new non
The Colin de Verdière graph parameter
, 1997
"... In 1990, Y. Colin de Verdière introduced a new graph parameter (G), based on spectral properties of matrices associated with G. He showed that (G) is monotone under taking minors and that planarity of G is characterized by the inequality (G) 3. Recently Lovasz and Schrijver showed that linkless emb ..."
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Cited by 24 (3 self)
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In 1990, Y. Colin de Verdière introduced a new graph parameter (G), based on spectral properties of matrices associated with G. He showed that (G) is monotone under taking minors and that planarity of G is characterized by the inequality (G) 3. Recently Lovasz and Schrijver showed that linkless
High dimensional graphs and variable selection with the Lasso
- ANNALS OF STATISTICS
, 2006
"... The pattern of zero entries in the inverse covariance matrix of a multivariate normal distribution corresponds to conditional independence restrictions between variables. Covariance selection aims at estimating those structural zeros from data. We show that neighborhood selection with the Lasso is a ..."
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Cited by 736 (22 self)
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show that the proposed neighborhood selection scheme is consistent for sparse high-dimensional graphs. Consistency hinges on the choice of the penalty parameter. The oracle value for optimal prediction does not lead to a consistent neighborhood estimate. Controlling instead the probability of falsely
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