Results 11 to 20 of about 63,637 (247)
On the First-Order Complexity of Induced Subgraph Isomorphism [PDF]
Logical Methods in Computer Science, 2019 Given a graph $F$, let $I(F)$ be the class of graphs containing $F$ as an induced subgraph. Let $W[F]$ denote the minimum $k$ such that $I(F)$ is definable in $k$-variable first-order logic.
Oleg Verbitsky, Maksim Zhukovskii
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Regular induced subgraphs of a random graph [PDF]
Random Structures & Algorithms, 2008 AbstractAn old problem of Erdős, Fajtlowicz, and Staton asks for the order of a largest induced regular subgraph that can be found in every graph on $n$ vertices. Motivated by this problem, we consider the order of such a subgraph in a typical graph on $n$ vertices, i.e., in a binomial random graph $G(n,1/2)$.
Michael Krivelevich +2 more
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Large induced subgraphs via triangulations and CMSO [PDF]
Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, 2013 We obtain an algorithmic meta-theorem for the following optimization problem. Let \phi\ be a Counting Monadic Second Order Logic (CMSO) formula and t be an integer. For a given graph G, the task is to maximize |X| subject to the following: there is a set
Fomin, Fedor +2 more
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Induced Subgraphs With Many Distinct Degrees [PDF]
Combinatorics, Probability and Computing, 2017 Let hom(G) denote the size of the largest clique or independent set of a graphG. In 2007, Bukh and Sudakov proved that everyn-vertex graphGwith hom(G) =O(logn) contains an induced subgraph with Ω(n1/2) distinct degrees, and raised the question of deciding whether an analogous result holds for everyn-vertex graphGwith hom(G) =O(nϵ), whereϵ> 0 is a ...
BHARGAV NARAYANAN, István Tomon
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Distinct degrees in induced subgraphs
Proceedings of the American Mathematical Society, 2019 An important theme of recent research in Ramsey theory has been establishing pseudorandomness properties of Ramsey graphs. An N N -vertex graph is called C C -Ramsey if it has no homogeneous set of size C log N C\log N .
Matthew Jenssen +3 more
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Enumerating Maximal Induced Subgraphs
, 2020 Given a graph $G$, the maximal induced subgraphs problem asks to enumerate all maximal induced subgraphs of $G$ that belong to a certain hereditary graph class. While its optimization version, known as the minimum vertex deletion problem in literature, has been intensively studied, enumeration algorithms are known for a few simple graph classes, e.g ...
Yixin Cao
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SEGCN: a subgraph encoding based graph convolutional network model for social bot detection [PDF]
Scientific ReportsMessage passing neural networks such as graph convolutional networks (GCN) can jointly consider various types of features for social bot detection. However, the expressive power of GCN is upper-bounded by the 1st-order Weisfeiler–Leman isomorphism test ...
Feng Liu +5 more
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Induced Subgraphs of Induced Subgraphs of Large Chromatic Number
Combinatorica, 2023 AbstractWe prove that, for every graph F with at least one edge, there is a constant $$c_F$$ c F such that there are graphs of arbitrarily large chromatic number and the same clique number as F in which every F-free induced subgraph has chromatic number at ...
Girao, A +6 more
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Induced star-triangle factors of graphs
Acta Universitatis Sapientiae: Mathematica, 2021 An induced star-triangle factor of a graph G is a spanning subgraph F of G such that each component of F is an induced subgraph on the vertex set of that component and each component of F is a star (here star means either K1,n, n ≥ 2 or K2) or a triangle
Kainth S. P. S., Kumar R., Pirzada S.
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On induced subgraphs of the cube [PDF]
Journal of Combinatorial Theory, Series A, 1988 Abstract Consider the usual graph Qn defined by the n-dimensional cube (having 2n vertices and n2n − 1 edges). We prove that if G is an induced subgraph of Qn with more than 2n − 1 vertices then the maximum degree in G is at least ( 1 2 − o(1)) log n . On the other hand, we construct an example which shows that this is not true for maximum
Zoltán Füredi +3 more
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