Results 101 to 110 of about 5,057 (262)
Enumerating Maximal Induced Subgraphs
CoRR, 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 ...
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Weak Degeneracy of Planar Graphs
Journal of Graph Theory, EarlyView.ABSTRACT The weak degeneracy of a graph G $G$ is a numerical parameter that was recently introduced by the first two authors with the aim of understanding the power of greedy algorithms for graph coloring. Every d $d$‐degenerate graph is weakly d $d$‐degenerate, but the converse is not true in general (e.g., all connected d $d$‐regular graphs except ...
Anton Bernshteyn +2 more
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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 Erdös +3 more
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Linear Versus Centred Colouring via Pseudogrids
Journal of Graph Theory, EarlyView.ABSTRACT A centred colouring of a graph is a vertex colouring in which every connected subgraph contains a vertex whose colour is unique and a linear colouring is a vertex colouring in which every (not‐necessarily induced) path contains a vertex whose colour is unique. For a graph G $G$, the centred chromatic number χ cen ( G ) ${\chi }_{\text{cen}}(G)$
Prosenjit Bose +4 more
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Characterizing paths graphs on bounded degree trees by minimal forbidden induced subgraphs [PDF]
, 2019 An undirected graph G is called a VPT graph if it is the vertex intersection graph of a family of paths in a tree. The class of graphs which admit a VPT representation in a host tree with maximum degree at most h is denoted by [h,2,1]. The classes [h,2,1]
Alcón, Liliana Graciela +2 more
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Journal of Graph Theory, EarlyView.ABSTRACT In an effort to understand the complexity of the maximum independent set problem, Chvátal introduced t‐perfect graphs. While a full characterization of this class remains open, important progress has been made for claw‐free graphs [Bruhn and Stein, Math. Program. 2012] and P 5 ${P}_{5}$‐free graphs [Bruhn and Fuchs, SIAM J. Discrete Math. 2017]
Yixin Cao, Shenghua Wang
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Computation of Graphlet Orbits for Nodes and Edges in Sparse Graphs
Journal of Statistical Software, 2016 Graphlet analysis is a useful tool for describing local network topology around individual nodes or edges. A node or an edge can be described by a vector containing the counts of different kinds of graphlets (small induced subgraphs) in which it appears,
Tomaž Hočevar, Janez Demšar
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Determining Graphs by the Complementary Spectrum
Discussiones Mathematicae Graph Theory, 2020 The complementary spectrum of a connected graph G is the set of the complementary eigenvalues of the adjacency matrix of G. In this note, we discuss the possibility of representing G using this spectrum.
Pinheiro Lucélia K. +2 more
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A structure theorem for graphs with no cycle with a unique chord and its consequences [PDF]
We give a structural description of the class C of graphs that do not contain a cycle with a unique chord as an induced subgraph. Our main theorem states that any connected graph in C is a either in some simple basic class or has a decomposition.
Nicolas Trotignon, Kristina Vuskovic
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A Linear Delay Algorithm for Enumerating All Connected Induced Subgraphs [PDF]
, 2018 Real biological and social data is increasingly being represented as graphs. Pattern-mining-based graph learning and analysis techniques report meaningful biological subnetworks that elucidate important interactions among entities.
Alokshiya, Mohammed
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