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Subgraph Isomorphism, log-Bounded Fragmentation and Graphs of (Locally) Bounded Treewidth [chapter]

MohammadTaghi Hajiaghayi, Naomi Nishimura
2002 Lecture Notes in Computer Science  
doi:10.1007/3-540-45687-2_25 fatcat:gkv72cv3hrgrbchhsgs6aklchy

Subgraph isomorphism, log-bounded fragmentation, and graphs of (locally) bounded treewidth

MohammadTaghi Hajiaghayi, Naomi Nishimura
2007 Journal of computer and system sciences (Print)  
doi:10.1016/j.jcss.2007.01.003 fatcat:nhpmqdcqtzhtbkb6bwhh4sycjy

Local certification of MSO properties for bounded treedepth graphs [article]

Nicolas Bousquet, Laurent Feuilloley, Théo Pierron
2021 arXiv   pre-print
In that direction, our main result states that any MSO formula can be locally certified on graphs with bounded treedepth with a logarithmic number of bits per node, which is the golden standard in certification  ...  We first investigate which properties can be locally certified with small certificates. Not surprisingly, this is almost never the case, except for not very expressive logic fragments.  ...  Can we certify with O(log n) bits that a graph G has treewidth at most t?  ... 
arXiv:2110.01936v1 fatcat:344p5alkczaxfgn7xnmm63ah2q

What Can Be Certified Compactly? Compact local certification of MSO properties in tree-like graphs

Laurent Feuilloley, Nicolas Bousquet, Théo Pierron
2022 Proceedings of the 2022 ACM Symposium on Principles of Distributed Computing  
More precisely, the logic we use is MSO, the most classic fragment for logics on graphs, where one can quantify over vertices and sets of vertices, and consider adjacency between vertices.  ...  We then move on to graphs of bounded treedepth, a well-known parameter that basically measures how far a graph is from a star.  ...  ACKNOWLEDGMENTS We thank Louis Esperet for fruitful discussions, Rotem Oshman for pointing out references about triangle-free graphs certification, Anca Muscholl for discussions about tree automata.  ... 
doi:10.1145/3519270.3538416 fatcat:4z2ials4ofhpblutphqq3o7mdm

Thin graph classes and polynomial-time approximation schemes [article]

Zdeněk Dvořák
2017 arXiv   pre-print
We also show that many graph classes (all proper minor-closed classes, and all subgraph-closed classes with bounded maximum degree and strongly sublinear separators) admit such decompositions.  ...  ., to all proper minor closed graph classes) are known, but they use a combination of techniques and usually focus on somewhat restricted classes of problems.  ...  Hence, this subgraph must have treewidth at most tw(H ′ ) ≤ t(r, 1). As the choice of G, v and r was arbitrary, we conclude that G has locally bounded treewidth.  ... 
arXiv:1704.00125v1 fatcat:62cftqx65bfq5bdsp6iyqisyfq

Two dichotomies for model-checking in multi-layer structures [article]

Jessica Enright, Kitty Meeks, Jessica Ryan
2020 arXiv   pre-print
Multi-layer graphs can capture qualitatively different types of connection between entities, and networks of this kind are prevalent in biological and social systems: for example, a social contact network  ...  or monadic second-order logic on the overall system, subject to the assumption that the structural properties are preserved under deletion of vertices and/or edges.  ...  Kitty Meeks is supported by a Royal Society of Edinburgh Personal Research Fellowship, funded by the Scottish Government. Jessica Ryan is supported by an EPSRC Doctoral Training Account.  ... 
arXiv:1710.08758v6 fatcat:nq5auk2cwjhafc6iqadsudlczy

Everything you always wanted to know about the parameterized complexity of Subgraph Isomorphism (but were afraid to ask) [article]

Dániel Marx, Michał Pilipczuk
2013 arXiv   pre-print
Given two graphs H and G, the Subgraph Isomorphism problem asks if H is isomorphic to a subgraph of G.  ...  On the hardness side, we present W[1]-hardness proofs under extremely restricted conditions, such as when H is a bounded-degree tree of constant pathwidth and G is a planar graph of bounded pathwidth.  ...  Model checking with a fixed first-order formula is known to be linear-time solvable on graphs of bounded local treewidth [28] , which implies that Subgraph Isomorphism can be solved in time f (|V (H)|  ... 
arXiv:1307.2187v3 fatcat:jbzjhag5d5cgdj6sed7q5hv4om

Testing Graph Isomorphism in Parallel by Playing a Game [article]

Martin Grohe, Oleg Verbitsky
2006 arXiv   pre-print
Using this approach, we prove that isomorphism of graphs of bounded treewidth is testable in TC1, answering an open question posed by Chandrasekharan.  ...  Furthermore, we obtain an AC1 algorithm for testing isomorphism of rotation systems (combinatorial specifications of graph embeddings).  ...  These include planar graphs [22] , graphs of bounded genus [18, 30] , graphs of bounded treewidth [9] , graphs with excluded minors [35] , graphs of bounded degree [29] , and graphs of bounded eigenvalue  ... 
arXiv:cs/0603054v1 fatcat:esegmdwmnfbjvizbqzszmlp4zq

Defective and Clustered Graph Colouring [article]

David R. Wood
2018 arXiv   pre-print
graph as an immersion, graphs with given thickness, graphs with given stack- or queue-number, graphs excluding K_t as a minor, graphs excluding K_s,t as a minor, and graphs excluding an arbitrary graph  ...  given subgraph, graphs with linear crossing number, linklessly or knotlessly embeddable graphs, graphs with given Colin de Verdière parameter, graphs with given circumference, graphs excluding a fixed  ...  I am particularly thankful to Frédéric Havet for allowing his unpublished proof of Lemma 29 to be included.  ... 
arXiv:1803.07694v1 fatcat:prcytiquyzb77cuxaexdflx5lm

Quantifying Systemic Evolutionary Changes by Color Coding Confidence-Scored PPI Networks [chapter]

Phuong Dao, Alexander Schönhuth, Fereydoun Hormozdiari, Iman Hajirasouliha, S. Cenk Sahinalp, Martin Ester
2009 Lecture Notes in Computer Science  
Following up on such a study, we compute the expected number of occurrences of non-induced subtrees with k ≤ 9 vertices.  ...  Beyond the previously reported differences between unicellular and multicellular organisms, we reveal major differences between prokaryotes and unicellular eukaryotes.  ...  Conclusions To quantify organismic complexity and evolutionary diversity from a systemic point of view poses challenging biological and computational problems.  ... 
doi:10.1007/978-3-642-04241-6_4 fatcat:hgna3xph75dbriowohshroemfu

Practical algorithms for MSO model-checking on tree-decomposable graphs

Alexander Langer, Felix Reidl, Peter Rossmanith, Somnath Sikdar
2014 Computer Science Review  
A straightforward implementation of the algorithm in the proof of Courcelle's Theorem is useless as it runs into space-explosion problems even for small values of treewidth.  ...  Of late, there have been several attempts to circumvent these problems and we review some of these in this survey.  ...  Graphs of locally bounded expansion include graphs of locally bounded treewidth and those locally excluding a minor [59] . Theorem 10 (Dvořák, Král, and Thomas [59] ).  ... 
doi:10.1016/j.cosrev.2014.08.001 fatcat:4eogxn65frdy5hr7syli5qjd5m

Logical complexity of graphs: a survey [article]

Oleg Pikhurko, Oleg Verbitsky
2013 arXiv   pre-print
We survey known estimates for these graph parameters and discuss their relations to other topics (such as the efficiency of the Weisfeiler-Lehman algorithm in isomorphism testing, the evolution of a random  ...  The logical depth D(G) of a graph G is equal to the minimum quantifier depth of a sentence defining G up to isomorphism.  ...  We are grateful to Joel Spencer for the fruitful collaboration on the subject of this survey and for allowing us to use his unpublished ideas in the proof of Lemma 6.8 and in Section 7.1.1.  ... 
arXiv:1003.4865v4 fatcat:pxpwl4gumbgfpmvsrrdx3z7u4i

Parameterized Extension Complexity of Independent Set and Related Problems [article]

Jakub Gajarský and Petr Hliněný and Hans Raj Tiwary
2017 arXiv   pre-print
While such results are not surprising since it is known that optimizing over STAB_k(G) is FPT for graphs of bounded expansion and W[1]-hard in general, they are also not trivial and in both cases stronger  ...  Let G be a graph on n vertices and STAB_k(G) be the convex hull of characteristic vectors of its independent sets of size at most k.  ...  and so F P T = W [t]. On the other hand, if the answer to (2) was no, then this would imply the existence of non-uniform FPT circuits for W [t]-complete problems which is considered unlikely.  ... 
arXiv:1511.08841v3 fatcat:ue2ukdwfynextpwxb3uch2vt4m

Counting perfect matchings in graphs that exclude a single-crossing minor [article]

Radu Curticapean
2014 arXiv   pre-print
Our algorithm uses black-boxes for counting perfect matchings in planar graphs and for computing certain graph decompositions.  ...  This is the first generalization of an algorithm for counting perfect matchings in K_3,3-free graphs (Little 1974, Vazirani 1989).  ...  Since structural results about graphs in C[H] for arbitrary (and not necessarily single-crossing) graphs H are known [15] , it is natural to ask whether our approach can be extended to such graphs.  ... 
arXiv:1406.4056v1 fatcat:lgd3r75qlnextddcmrdnm47vly

Parameterized Complexity and Biopolymer Sequence Comparison

L. Cai, X. Huang, C. Liu, F. Rosamond, Y. Song
2007 Computer journal  
The article surveys parameterized algorithms and complexities for computational tasks on biopolymer sequences, including the problems of longest common subsequence, shortest common supersequence, pairwise  ...  sequence alignment, multiple sequencing alignment, structure-sequence alignment, and structure-structure alignment.  ...  The output is a subgraph G of G and the optimal isomorphic mapping. The small treewidth of the structure graph does not make Generalized Subgraph Isomorphism easy.  ... 
doi:10.1093/comjnl/bxm035 fatcat:nycuqgahm5fibhrwhoqjw4tcke
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