Results 31 to 40 of about 1,191,800 (264)
Extremal Statistics on Non-Crossing Configurations [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We obtain several properties of extremal statistics in non-crossing configurations with n vertices. We prove that the maximum degree and the largest component are of logarithmic order, and the diameter is of order $\sqrt{n}$.
Anna Mier, Marc Noy
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Reducing the maximum degree of a graph by deleting vertices: the extremal cases
Theory and Applications of Graphs, 2018 Let $\lambda(G)$ denote the smallest number of vertices that can be removed from a non-empty graph $G$ so that the resulting graph has a smaller maximum degree. In a recent paper, we proved that if $n$ is the number of vertices of $G$, $k$ is the maximum
Peter Borg, Kurt Fenech
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CoRR, 2016 A graph H is a square root of a graph G if G can be obtained from H by adding an edge between any two vertices in H that are of distance 2. The Square Root problem is that of deciding whether a given graph admits a square root. This problem is only known to be NP-complete for chordal graphs and polynomial-time solvable for non-trivial minor-closed ...
Manfred Cochefert +5 more
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The Overfullness of Graphs with Small Minimum Degree and Large Maximum Degree
SIAM Journal on Discrete Mathematics, 2022 One portion of arXiv:2005.12909 is incorporated into this paper.
Yan Cao 0001 +3 more
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Computing a maximal clique of graphs of cofinite submonoids [PDF]
Notes on Number Theory and Discrete MathematicsA graph G𝔰 is called an 𝔰(τ,e)-graph if there exists a numerical semigroup 𝔰 with multiplicity τ and embedding dimension e such that V(G𝔰)={v_α : α ∈ℕ₀\𝔰} and E(G𝔰)={v_αv_β⇔α+β∈𝔰}.
Anam Shahzadi, Muhammad Ahsan Binyamin
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Maximum average degree of list-edge-critical graphs and Vizing's conjecture
Electronic Journal of Graph Theory and Applications, 2022 Vizing conjectured that χ′ℓ(G)≤Δ + 1 for all graphs. For a graph G and nonnegative integer k, we say G is a k-list-edge-critical graph if χ′ℓ(G)>k, but χ′ℓ(G − e)≤k for all e ∈ E(G).
Joshua Harrelson, Hannah Reavis
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The maximum number of triangles in a graph of given maximum degree [PDF]
Advances in Combinatorics, 2020 Maximizing or minimizing the number of copies of a fixed graph in a large host graph is one of the most classical topics in extremal graph theory. Indeed, one of the most famous problems in extremal graph theory, the Erdős-Rademacher problem, which can be traced back to the 1940s, asks to determine the minimum number of triangles in a graph with a ...
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Eccentricity of Networks with Structural Constraints
Discussiones Mathematicae Graph Theory, 2020 The eccentricity of a node v in a network is the maximum distance from v to any other node. In social networks, the reciprocal of eccentricity is used as a measure of the importance of a node within a network.
Krnc Matjaž +3 more
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Maximum Reciprocal Degree Resistance Distance Index of Bicyclic Graphs
Discrete Dynamics in Nature and Society, 2021 The reciprocal degree resistance distance index of a connected graph G is defined as RDRG=∑u,v⊆VGdGu+dGv/rGu,v, where rGu,v is the resistance distance between vertices u and v in G. Let ℬn denote the set of bicyclic graphs without common edges and with n
Gaixiang Cai, Xing-Xing Li, Guidong Yu
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On the Maximum Degree of a Random Planar Graph
Combinatorics, Probability and Computing, 2008 Let the random graphRnbe drawn uniformly at random from the set of all simple planar graphs onnlabelled vertices. We see that with high probability the maximum degree ofRnis Θ(lnn). We consider also the maximum size of a face and the maximum increase in the number of components on deleting a vertex.
McDiarmid, C, Reed, B
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