Results 41 to 50 of about 59,275 (246)
Application of an Extremal Result of Erdős and Gallai to the (n,k,t) Problem
Theory and Applications of Graphs, 2017 An extremal result about vertex covers, attributed by Hajnal to Erdős and Gallai, is applied to prove the following: If n, k, and t are integers satisfying n ≥ k ≥ t ≥ 3 and k ≤ 2t - 2, and G is a graph with the minimum number of edges among graphs on n ...
Matt Noble +3 more
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A note on the generator subgraph of a graph
Electronic Journal of Graph Theory and Applications, 2020 Graphs considered in this paper are finite simple undirected graphs. Let G = (V(G), E(G)) be a graph with E(G) = {e1, e2,..., em}, for some positive integer m. The edge space of G, denoted by ℰ(G), is a vector space over the field ℤ2. The elements of ℰ(
Neil Mores Mame +1 more
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Finding Induced Subgraphs via Minimal Triangulations [PDF]
, 2009 Potential maximal cliques and minimal separators are combinatorial objects which were introduced and studied in the realm of minimal triangulations problems including Minimum Fill-in and Treewidth.
Fomin, Fedor V., Villanger, Yngve
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Induced subgraphs of given sizes
Discrete Mathematics, 1999 This paper considers certain ``natural'' generalizations of ``Turán-type'' extremal problems investigated earlier by \textit{P. Erdős} [Extremal problems in graph theory. Theory Graphs Appl., Proc. Symp. Smolenice 1963, 29-36 (1964; Zbl 0161.20501)] and by \textit{P. Erdős, V. T. Sós}, and the reviewer [Some extremal problems on \(r\)-graphs.
Paul Erdős +3 more
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Reconfiguration of Regular Induced Subgraphs
, 2022 We study the problem of checking the existence of a step-by-step transformation of $d$-regular induced subgraphs in a graph, where $d \ge 0$ and each step in the transformation must follow a fixed reconfiguration rule. Our problem for $d=0$ is equivalent to \textsc{Independent Set Reconfiguration}, which is one of the most well-studied reconfiguration ...
Hiroshi Eto +4 more
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Ore- and Fan-type heavy subgraphs for Hamiltonicity of 2-connected graphs
, 2013 Bedrossian characterized all pairs of forbidden subgraphs for a 2-connected graph to be Hamiltonian. Instead of forbidding some induced subgraphs, we relax the conditions for graphs to be Hamiltonian by restricting Ore- and Fan-type degree conditions on ...
Bedrossian +13 more
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The complexity of the connected graph access structure on seven participants
Journal of Mathematical Cryptology, 2017 In this paper, we study an important problem in secret sharing that determines the exact value or bound for the complexity. First, we use the induced subgraph complexity of the graph G with access structure Γ to obtain a lower bound on the complexity of ...
Hadian Dehkordi Massoud, Safi Ali
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Forbidden subgraph pairs for traceability of block-chains
Electronic Journal of Graph Theory and Applications, 2013 A block-chain is a graph whose block graph is a path, i.e. it is either a $P_1$, a $P_2$, or a 2-connected graph, or a graph of connectivity 1 with exactly two end-blocks. A graph is called traceable if it contains a Hamilton path.
Binlong Li +2 more
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Matched Filters for Noisy Induced Subgraph Detection [PDF]
, 2018 The problem of finding the vertex correspondence between two noisy graphs with different number of vertices where the smaller graph is still large has many applications in social networks, neuroscience, and computer vision.
Lyzinski, Vince +3 more
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Graphs with distinguishing sets of size k
Kuwait Journal of ScienceThe size of a resolving set R of a non-trivial connected graph Γ of order n ≥ 2 is the number of edges in the induced subgraph .The minimum cardinality of a resolving set of size k of graph Γ is called the metric dimension of size k, denoted by β(k)(Γ ...
Muhammad Naeem Azhar +3 more
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