Results 31 to 40 of about 34,901 (303)
Finding a heaviest vertex-weighted triangle is not harder than matrix multiplication [PDF]
, 2009 We show that a maximum-weight triangle in an undirected graph with n vertices and real weights assigned to vertices can be found in time O(n(omega) + n(2+o(1))), where omega is the exponent of the fastest matrix multiplication algorithm. By the currently
Lingas, Andrzej, +4 more
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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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Triangle-free graphs which are minimal for some nonstable 4-vertex subset
Arab Journal of Mathematical Sciences, 2015 In a graph G, a module is a vertex subset M such that every vertex outside M is adjacent to all or none of M. A graph G is prime if ϕ, the single-vertex sets, and V(G) are the only modules in G.
Mohammad Alzohairi
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Laplacian Spectral Properties of Signed Circular Caterpillars
Theory and Applications of Graphs, 2020 A circular caterpillar of girth $n$ is a graph such that the removal of all pendant vertices yields a cycle $C_n$ of order $n$. A signed graph is a pair $\Gamma=(G, \sigma)$, where $G$ is a simple graph and $\sigma: E(G) \rightarrow \{+1, -1\}$ is the ...
Maurizio Brunetti
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Triangle-Free Planar Graphs as Segment Intersection Graphs [PDF]
, 2002 We prove that every triangle-free planar graph is the intersection graph of a set of segments in the plane. Moreover, the segments can be chosen in only three directions (horizontal, vertical and oblique) and in such a way that no two segments cross ...
Cobos Gavala, Javier +4 more
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Colored complete hypergraphs containing no rainbow Berge triangles
Theory and Applications of Graphs, 2019 The study of graph Ramsey numbers within restricted colorings, in particular forbidding a rainbow triangle, has recently been blossoming under the name Gallai-Ramsey numbers.
Colton Magnant
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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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On the Circumference of 3-Connected Cubic Triangle-Free Plane Graphs
Journal of Mathematics, 2021 The circumference of a graph G is the length of a longest cycle in G, denoted by cirG. For any even number n, let cn = min {cirG|G is a 3-connected cubic triangle-free plane graph with n vertices}. In this paper, we show that an upper bound of cn is n+1−
Adthasit Sinna +2 more
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Simplifying social networks via triangle-based cohesive subgraphs
Visual Informatics, 2023 One main challenge for simplifying node-link diagrams of large-scale social networks lies in that simplified graphs generally contain dense subgroups or cohesive subgraphs.
Rusheng Pan +6 more
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Decomposing Graphs into Edges and Triangles [PDF]
Combinatorics, Probability and Computing, 2019 We prove the following 30 year-old conjecture of Győri and Tuza: the edges of every n-vertex graph G can be decomposed into complete graphs C1,. . .,Cℓ of orders two and three such that |C1|+···+|Cℓ| ≤ (1/2+o(1))n2. This result implies the asymptotic version of the old result of Erdős, Goodman and Pósa that asserts the existence of such a decomposition
Daniel Král' +3 more
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