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Evasiveness of Subgraph Containment and Related Properties

Amit Chakrabarti, Subhash Khot, Yaoyun Shi
2001 SIAM journal on computing (Print)  
For the property of containing a subgraph isomorphic to a fixed graph, and a fairly large class of related n-vertex graph properties, we show evasiveness for an arithmetic progression of values of n.  ...  We prove new results on evasiveness of monotone graph properties by extending the techniques of Kahn, Saks, and Sturtevant [Combinatorica, 4 (1984), pp. 297-306].  ...  We would like to express our sincere thanks to Professors Sanjeev Arora, Bernard Chazelle, and Andrew Yao for their valuable comments and suggestions.  ... 
doi:10.1137/s0097539700382005 fatcat:hwgo4fvwn5fsvfm3osjxhut5qi

Evasiveness of Subgraph Containment and Related Properties [chapter]

Amit Chakrabarti, Subhash Khot, Yaoyun Shi
2001 Lecture Notes in Computer Science  
For the property of containing a subgraph isomorphic to a fixed graph, and a fairly large class of related n-vertex graph properties, we show evasiveness for an arithmetic progression of values of n.  ...  We prove new results on evasiveness of monotone graph properties by extending the techniques of Kahn, Saks, and Sturtevant [Combinatorica, 4 (1984), pp. 297-306].  ...  We would like to express our sincere thanks to Professors Sanjeev Arora, Bernard Chazelle, and Andrew Yao for their valuable comments and suggestions.  ... 
doi:10.1007/3-540-44693-1_10 fatcat:rcsqupujuzdobdqwnmnexefwka

Page 1318 of Mathematical Reviews Vol. , Issue 2003B [page]

2003 Mathematical Reviews  
of subgraph containment and related properties.  ...  For the property of containing a subgraph isomorphic to a fixed graph, and a fairly large class of related n-vertex graph properties, we show evasiveness for an arithmetic 68 COMPUTER SCIENCE 1318 progression  ... 

Page 2318 of Mathematical Reviews Vol. , Issue 86f [page]

1986 Mathematical Reviews  
A property is said to be evasive if every entry of the matrix must be examined. Karp conjectured that every nontrivial graph property preserved by addition of edges is evasive.  ...  A class C of graphs closed with respect to categorical products and to induced subgraphs is called a productive hereditary class of graphs.  ... 

Counting Induced Subgraphs: A Topological Approach to #W[1]-hardness

Marc Roth, Johannes Schmitt
2020 Algorithmica  
We investigate the problem # IndSub ( Φ ) of counting all induced subgraphs of size k in a graph G that satisfy a given property Φ .  ...  This continues the work of Jerrum and Meeks who proved the problem to be # W [ 1 ] -hard for some families of properties which include (dis)connectedness [JCSS 15] and even- or oddness of the number of  ...  Furthermore we wish to point out that Sloane's OEIS [1] was very useful in the course of this work.  ... 
doi:10.1007/s00453-020-00676-9 pmid:32801408 pmcid:PMC7416760 fatcat:s7i4a6yrtjd43okvw3r4cmreqe

The Evasiveness Conjecture and Graphs on 2p Vertices [article]

Andres Angel, Jerson Borja
2016 arXiv   pre-print
In this paper we study the size of the automorphism group of a graph on 2p vertices to estimate the Euler characteristic of monotone non-evasive graph properties and get some conditions such graph properties  ...  The Evasiveness conjecture have been proved for properties of graphs on a prime-power number of vertices and the six vertices case. The ten vertices case is still unsolved.  ...  The ingenious approach of Kahn, Saks and Sturtevant [5] permitted to solve the prime-power case and gave new directions on how to attack various related problems to the evasiveness conjecture.  ... 
arXiv:1603.04412v1 fatcat:2ccjlkovo5gupee4qu67ajdip4

Graph properties in node-query setting: effect of breaking symmetry [article]

Nikhil Balaji, Samir Datta, Raghav Kulkarni, Supartha Podder
2015 arXiv   pre-print
We show that the answer is no for any hereditary property with finitely many forbidden subgraphs by exhibiting a bound of Ω(n^1/k) for some constant k depending only on the property.  ...  In this setting a graph G = (V, E) on n vertices and a property P are given. A black-box access to an unknown subset S ⊆ V is provided via queries of the form 'Does i ∈ S?'.  ...  Section 3 contains Weak Evasiveness results under symmetry. Section 4 contains proofs of Theorem 1.2 and Theorem 1.4.  ... 
arXiv:1510.08267v1 fatcat:m6iegnep2nhbxh5jm63zxfj2q4

Further results on the Aanderaa-Rosenberg conjecture

D.J Kleitman, D.J Kwiatkowski
1980 Journal of combinatorial theory. Series B (Print)  
Some results on the "evasiveness" of graph properties are obtained, extending the work of Rivest and Vuillemin.  ...  In particular, it is shown that any nontrivial monotone graph property on IZ vertices is at least na/9-evasive; particular stronger results are obtained for values of II that are powers of primes less  ...  Rivest and V. Boas for stimulating J. Griggs for many valuable suggestions and editorial assistance.  ... 
doi:10.1016/0095-8956(80)90057-x fatcat:j4zegjzoovb4pbyhy4r4azfhjy

A hierarchy of dismantlings in Graphs [article]

Etienne Fieux, Bertrand Jouve
2020 arXiv   pre-print
We point out how these higher dismantlabilities are related to the derivability of graphs defined by Mazurkievicz and we get a new characterization of the class of closed graphs he defined.  ...  By generalising the notion of vertex transitivity, we consider the issue of higher dismantlabilities in link with the evasiveness conjecture.  ...  Vertex-transitive graphs, k-dismantlability and evasivity The relation E defined on the set V pXq of vertices of a graph X by x E y ðñ N X rxs " N X rys is an equivalence relation whose equivalence classes  ... 
arXiv:1902.04508v2 fatcat:f4wrdrnor5hglig32g577wiclm

Counting Induced Subgraphs: A Topological Approach to #W[1]-hardness [article]

Marc Roth, Johannes Schmitt
2018 arXiv   pre-print
We investigate the problem #IndSub(Φ) of counting all induced subgraphs of size k in a graph G that satisfy a given property Φ.  ...  This continues the work of Jerrum and Meeks who proved the problem to be #W[1]-hard for some families of properties which include, among others, (dis)connectedness [JCSS 15] and even- or oddness of the  ...  Acknowledgements We are very grateful to Cornelius Brand, Radu Curticapean, Holger Dell and Johannes Lengler for helpful advice and fruitful discussions.  ... 
arXiv:1807.01920v1 fatcat:vm4x4zmuo5g5veh5uxn7io3ov4

A note on independence complexes of chordal graphs and dismantling [article]

Michal Adamaszek
2015 arXiv   pre-print
The proof uses the properties of tree models of chordal graphs.  ...  We show that the independence complex of a chordal graph is contractible if and only if this complex is dismantlable (strong collapsible) and it is homotopy equivalent to a sphere if and only if its core  ...  of T which contain v form a subtree of T , (c) vw ∈ E(G) if and only if there is a node of T containing both v and w.  ... 
arXiv:1508.02426v1 fatcat:bmvsjzma65dcdhrjhpc3tflqcq

Counting Induced Subgraphs: An Algebraic Approach to #W[1]-hardness

Julian Dörfler, Marc Roth, Johannes Schmitt, Philip Wellnitz, Michael Wagner
2019 International Symposium on Mathematical Foundations of Computer Science  
We study the problem #IndSub(Φ) of counting all induced subgraphs of size k in a graph G that satisfy the property Φ.  ...  Very recently [IPEC 18], two of the authors introduced a novel technique for the complexity analysis of #IndSub(Φ), inspired by the "topological approach to evasiveness" of Kahn, Saks and Sturtevant [FOCS  ...  As a next step towards a proof of Conjecture 1, we suggest the study of properties that are defined by forbidden induced subgraphs, for which the complexity of #IndSub(Φ) is only partially resolved at  ... 
doi:10.4230/lipics.mfcs.2019.26 dblp:conf/mfcs/DorflerRSW19 fatcat:n4mlfouyavbchdyt5sedb5amfq

Transferable Graph Backdoor Attack [article]

Shuiqiao Yang, Bao Gia Doan, Paul Montague, Olivier De Vel, Tamas Abraham, Seyit Camtepe, Damith C. Ranasinghe, Salil S. Kanhere
2022 arXiv   pre-print
Despite the success of GNNs, and similar to other types of deep neural networks, GNNs are found to be vulnerable to unnoticeable perturbations on both graph structure and node features.  ...  The core attack principle is to poison the training dataset with perturbation-based triggers that can lead to an effective and transferable backdoor attack.  ...  ACKNOWLEDGMENTS This research was supported by Next Generation Technologies Fund programme with the Defence Science and Technology Group, Australia.  ... 
arXiv:2207.00425v2 fatcat:i55ezhpivfha3bh3sijz5dbjxm

Guarding a subgraph as a tool in pursuit-evasion games

Drago Bokal, Janja Jerebic
2019 Discussiones Mathematicae Graph Theory  
Pursuit-evasion games study the number of cops needed to capture the robber in a game played on a graph, in which the cops and the robber move alternatively to neighbouring vertices, and the robber is  ...  In some cases, this implies a polynomially computable certification of the negative answer to the NP-complete problem of existence of a retraction to a given subgraph.  ...  This work was in part supported by the Ministry of Science of Slovenia under the grant P1-0297 and research projects J1-8130, L7-5459, N1-0057 of ARRS (Slovenia).  ... 
doi:10.7151/dmgt.2244 fatcat:wdsc4myqgbcivj7iuo62wdn2v4

A topological approach to evasiveness

Jeff Kahn, Michael Saks, Dean Sturtevant
1984 Combinatorica  
Karp conjectured that every such property is evasive, i.e., requires that every entry of the incidence matrix be examined.  ...  Rivest and Vuillemin proved the result (conjectured by Aanderaa and Rosenberg) that every graph property that is monotone (preserved by addition of edges) and nontrivial (holds for some but not all graphs  ...  Analogous definitions can be made for (isomorphism-invariant) properties of undirected graphs---henceforth graph properties--and in particular such a property is evasive if its complexity is 1~1.  ... 
doi:10.1007/bf02579140 fatcat:wmx24dtqjvfg7g5amsijweow64
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