Results 11 to 20 of about 31,664 (169)
On the independence number of intersection graphs of axis-parallel segments
Journal of Computational Geometry, 2023 We prove that for any triangle-free intersection graph of $n$ axis-parallel line segments in the plane, the independence number $\alpha$ of this graph is at least $\alpha \ge n/4 + \Omega(\sqrt{n})$.
Marco Caoduro +3 more
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On distances and metrics in discrete ordered sets [PDF]
Mathematica Bohemica, 2021 Discrete partially ordered sets can be turned into distance spaces in several ways. The distance functions may or may not satisfy the triangle inequality and restrictions of the distance to finite chains may or may not coincide with the natural ...
Stephan Foldes, Sándor Radeleczki
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The Spectrum of Triangle-Free Graphs
SIAM Journal on Discrete Mathematics, 2023 Denote by $q_n(G)$ the smallest eigenvalue of the signless Laplacian matrix of an $n$-vertex graph $G$. Brandt conjectured in 1997 that for regular triangle-free graphs $q_n(G) \leq \frac{4n}{25}$. We prove a stronger result: If $G$ is a triangle-free graph then $q_n(G) \leq \frac{15n}{94}< \frac{4n}{25}$.
József Balogh +4 more
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Families of Integral Cographs within a Triangular Array
Special Matrices, 2020 The determinant Hosoya triangle, is a triangular array where the entries are the determinants of two-by-two Fibonacci matrices. The determinant Hosoya triangle mod 2 gives rise to three infinite families of graphs, that are formed by complete product ...
Ching Hsin-Yun +2 more
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Decompositions of triangle-dense graphs [PDF]
Proceedings of the 5th conference on Innovations in theoretical computer science, 2014 High triangle density -- the graph property stating that a constant fraction of two-hop paths belong to a triangle -- is a common signature of social networks. This paper studies triangle-dense graphs from a structural perspective. We prove constructively that significant portions of a triangle-dense graph are contained in a disjoint union of dense ...
Rishi Gupta +2 more
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Sufficient conditions for triangle-free graphs to be super-$λ'$ [PDF]
Transactions on Combinatorics, 2018 An edge-cut $F$ of a connected graph $G$ is called a restricted edge-cut if $G-F$ contains no isolated vertices. The minimum cardinality of all restricted edge-cuts is called the restricted edge-connectivity $λ'(G)$ of $G$. A graph $G$ is said to
Huiwen Cheng, Yan-Jing Li
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The recognition of triangle graphs [PDF]
Theoretical Computer Science, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On triangle cover contact graphs [PDF]
Computational Geometry, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shaheena Sultana +4 more
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Sparse sets in triangle-free graphs [PDF]
Mathematica BohemicaA set of vertices is $k$-sparse if it induces a graph with a maximum degree of at most $k$. In this missive, we consider the order of the largest $k$-sparse set in a triangle-free graph of fixed order. We show, for example, that every triangle-free graph
Tınaz Ekim +2 more
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Planar graphs with $\Delta \geq 7$ and no triangle adjacent to a $C_4$ are minimally edge and total choosable [PDF]
Discrete Mathematics & Theoretical Computer Science, 2016 For planar graphs, we consider the problems of list edge coloring and list total coloring. Edge coloring is the problem of coloring the edges while ensuring that two edges that are adjacent receive different colors.
Marthe Bonamy +2 more
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