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Triangle Factors in Random Graphs
Combinatorics, Probability and Computing, 1997For a graph G=(V, E) on n vertices, where 3 divides n, a triangle factor is a subgraph of G, consisting of n/3 vertex disjoint triangles (complete graphs on three vertices). We discuss the problem of determining the minimal probability p=p(n), for which a random graph G∈[Gscr ](n, p) contains almost surely a triangle factor.
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On the Minimal Density of Triangles in Graphs
Combinatorics, Probability and Computing, 2008For a fixed ρ ∈ [0, 1], what is (asymptotically) the minimal possible density g3(ρ) of triangles in a graph with edge density ρ? We completely solve this problem by proving thatwhere$t\df \lfloor 1/(1-\rho)\rfloor$is the integer such that$\rho\in\bigl[ 1-\frac 1t,1-\frac 1{t+1}\bigr]$.
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On the Evolution of Triangle-Free Graphs
Combinatorics, Probability and Computing, 2005Let ${\cal T}(n,m)$ denote the set of all labelled triangle-free graphs with $n$ vertices and exactly $m$ edges. In this paper we give a short self-contained proof of the fact that there exists a constant $C>0$ such that, for all $m\geq Cn^{3/2}\sqrt{\log n}$, a graph chosen uniformly at random from ${\cal T}(n,m)$ is with probability $1-o(1 ...
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Independent sets in graphs with triangles
Information Processing Letters, 1996zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Thomas Hofmeister, Hanno Lefmann
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On regular triangle-distinct graphs
Computational and Applied MathematicszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dragan Stevanovic +4 more
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On triangle-free random graphs
Random Structures and Algorithms, 2000An \((n,M)\)-graph is a graph with \(n\) labeled vertices and \(M\) edges. It was shown by Prömel and Steger that if \(M = |\Omega (n^{7/4}\log n)|\) then with high probability a graph chosen uniformly at random from among all triangle-free \((n,M)\)-graphs is bipartite. They conjectured that the same should be true when \(M \geq n^{3/2 + \varepsilon}\)
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Structured encryption for triangle counting on graph data
Future Generation Computer Systems, 2023Lanxiang Chen
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Fast and Scalable Triangle Counting in Graph Streams: The Hybrid Approach
Lecture Notes in Networks and Systems, 2021Venkaṭesh Srinivasan +2 more
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On distance-regular graphs Γ of diameter 3 for which Γ 3 is a triangle-free graph
Discrete Mathematics and Applications, 2023Wenbin Guo
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CoCoS: Fast and Accurate Distributed Triangle Counting in Graph Streams
ACM Transactions on Knowledge Discovery From Data, 2021Kijung Shin +2 more
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