Results 11 to 20 of about 1,191,800 (264)
Local boxicity and maximum degree
Discrete Mathematics, 2022 17 ...
Atrayee Majumder, Rogers Mathew
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The maximum likelihood degree [PDF]
American Journal of Mathematics, 2006 Maximum likelihood estimation in statistics leads to the problem of maximizing a product of powers of polynomials. We study the algebraic degree of the critical equations of this optimization problem. This degree is related to the number of bounded regions in the corresponding arrangement of hypersurfaces, and to the Euler characteristic of the ...
Catanese, Fabrizio +3 more
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Acyclic Coloring of Graphs of Maximum Degree $\Delta$ [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 An acyclic coloring of a graph $G$ is a coloring of its vertices such that: (i) no two neighbors in $G$ are assigned the same color and (ii) no bicolored cycle can exist in $G$.
Guillaume Fertin, André Raspaud
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Reducing the maximum degree of a graph: comparisons of bounds
Theory and Applications of Graphs, 2021 Let $\lambda(G)$ be 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.
Peter Borg
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Strong Immersions and Maximum Degree [PDF]
SIAM Journal on Discrete Mathematics, 2014 10 ...
Zdenek Dvorák 0001, Tereza Klimosová
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Random Graphs with a Fixed Maximum Degree [PDF]
SIAM Journal on Discrete Mathematics, 2020 We study the component structure of the random graph $G=G_{n,m,d}$. Here $d=O(1)$ and $G$ is sampled uniformly from ${\mathcal G}_{n,m,d}$, the set of graphs with vertex set $[n]$, $m$ edges and maximum degree at most $d$. If $m=μn/2$ then we establish a threshold value $μ_\star$ such that if $μμ_\star$ then w.h.p.
Alan M. Frieze, Tomasz Tkocz
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The Maximum Degree of Series-Parallel Graphs [PDF]
Combinatorics, Probability and Computing, 2011 We prove that the maximum degree Δnof a random series-parallel graph withnvertices satisfies Δn/logn→cin probability, andΔn~clognfor a computable constantc> 0. The same kind of result holds for 2-connected series-parallel graphs, for outerplanar graphs, and for 2-connected outerplanar graphs.
Drmota, Michael +2 more
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Journal of Combinatorial Theory, Series B, 2008 An axis-parallel $d$--dimensional box is a Cartesian product $R_1 \times R_2 \times ... \times R_d$ where $R_i$ (for $1 \le i \le d$) is a closed interval of the form $[a_i, b_i]$ on the real line. For a graph $G$, its \emph{boxicity} $\boxi(G)$ is the minimum dimension $d$, such that $G$ is representable as the intersection graph of (axis--parallel ...
Chandran, L Sunil +2 more
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Chromatic index, treewidth and maximum degree [PDF]
Electronic Notes in Discrete Mathematics, 2016 We conjecture that any graph $G$ with treewidth $k$ and maximum degree $\Delta(G)\geq k + \sqrt{k}$ satisfies $\chi'(G)=\Delta(G)$. In support of the conjecture we prove its fractional version. We also show that any graph $G$ with treewidth $k\geq 4$ and maximum degree $2k-1$ satisfies $\chi'(G)=\Delta(G)$, extending an old result of Vizing.
Henning Bruhn +2 more
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Equating κ Maximum Degrees in Graphs without Short Cycles
Discussiones Mathematicae Graph Theory, 2020 For an integer k at least 2, and a graph G, let fk(G) be the minimum cardinality of a set X of vertices of G such that G − X has either k vertices of maximum degree or order less than k.
Fürst Maximilian +4 more
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