Results 21 to 30 of about 31,664 (169)
Universality of Graphs with Few Triangles and Anti-Triangles [PDF]
Combinatorics, Probability and Computing, 2015 We study 3-random-likegraphs, that is, sequences of graphs in which the densities of triangles and anti-triangles converge to 1/8. Since the random graph$\mathcal{G}$n,1/2is, in particular, 3-random-like, this can be viewed as a weak version of quasi-randomness.
Dan Hefetz, Mykhaylo Tyomkyn
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On vertex and edge degree-based topological indices
Vojnotehnički Glasnik, 2023 Introduction/purpose: The entire topological indices (T Ient) are a class of graph invariants depending on the degrees of vertices and edges. Some general properties of these invariants are established.
Ivan Gutman
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On Touching Triangle Graphs [PDF]
, 2011 In this paper, we consider the problem of representing graphs by triangles whose sides touch. As a simple necessary condition, we show that pairs of vertices must have a small common neighborhood. On the positive side, we present linear time algorithms for creating touching triangle representations for outerplanar graphs, square grid graphs, and ...
Emden R. Gansner +2 more
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On hamiltonicity of 1-tough triangle-free graphs
Electronic Journal of Graph Theory and Applications, 2021 Let ω(G) denote the number of components of a graph G. A connected graph G is said to be 1-tough if ω(G − X)≤|X| for all X ⊆ V(G) with ω(G − X)>1. It is well-known that every hamiltonian graph is 1-tough, but that the reverse statement is not true in ...
Wei Zheng, Hajo Broersma, Ligong Wang
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Discrete Analysis, 2020 An efficient container lemma, Discrete Analysis 2020:17, 56 pp. The hypergraph container lemma, discovered independently in 2012 by David Saxton and Andrew Thomason, and by József Balogh, Robert Morris and Wojciech Samotij, is an extremely powerful tool
Jozsef Balogh, Wojciech Samotij
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Discrete Mathematics, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Martin Loebl +2 more
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Journal of Graph Algorithms and Applications, 2011 In this work, we introduce the notion of triangle sparsifiers, i.e., sparse graphs which are approximately the same to the original graph with respect to the triangle count.
Charalampos Tsourakakis +2 more
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Graphing trillions of triangles [PDF]
Information Visualization, 2016 The increasing size of Big Data is often heralded but how data are transformed and represented is also profoundly important to knowledge discovery, and this is exemplified in Big Graph analytics. Much attention has been placed on the scale of the input graph but the product of a graph algorithm can be many times larger than the input.
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AKCE International Journal of Graphs and Combinatorics, 2018 Let G be a 4-connected graph, and let E ̃ (G) denote the set of those edges of G which are not contained in a triangle, and let E c (G) denote the set of 4-contractible edges of G . We show that if 3 ≤ | E ̃ (G) | ≤ 4 or | E ̃ (G) | ≥ 7 , then | E c (G) |
Yoshimi Egawa +2 more
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COMICS: a community property-based triangle motif clustering scheme [PDF]
PeerJ Computer Science, 2019 With the development of science and technology, network scales of various fields have experienced an amazing growth. Networks in the fields of biology, economics and society contain rich hidden information of human beings in the form of connectivity ...
Yufan Feng +4 more
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