Results 31 to 40 of about 31,664 (169)
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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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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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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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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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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Packing Triangles in Weighted Graphs [PDF]
SIAM Journal on Discrete Mathematics, 2014 v2: 20 pages, corrected version (from 2013) following referee ...
Chapuy, Guillaume +4 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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Straight-Line Triangle Representations via Schnyder Labelings
Journal of Graph Algorithms and Applications, 2015 A straight-line triangle representation (SLTR) of a planar graph is a straight-line drawing such that all the faces including the outer face are triangles. Such a drawing can be viewed as a tiling of a triangle with triangles where the input graph is the
Nieke Aerts, Stefan Felsner
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Triangle-degree and triangle-distinct graphs
Discrete MathematicsLet $G$ be a simple graph and $v$ be a vertex of $G$. The triangle-degree of $v$ in $G$ is the number of triangles that contain $v$. While every graph has at least two vertices with the same degree, there are graphs in which every vertex has a distinct triangle-degree. In this paper, we construct an infinite family of graphs with this property. We also
Zhanar Berikkyzy +7 more
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Edge Bounds and Degeneracy of Triangle-Free Penny Graphs and Squaregraphs
Journal of Graph Algorithms and Applications, 2018 We show that triangle-free penny graphs have degeneracy at most two, and that both triangle-free penny graphs and squaregraphs have at most $\min\bigl(2n-\Omega(\sqrt n),2n-D-2\bigr)$ edges, where $n$ is the number of vertices and $D$ is the diameter of ...
David Eppstein
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