Graph Theory: Lecture No. 28
The minimum integer ksuch that Gcan be
represented as the intersection graph of some
family of axis-parallel k-dimensional boxes is
called the boxicity of G.
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Graph Theory: Intersection Graphs and Hamilton Cycles in Graphs, Slides of Design and Analysis of Algorithms
Two important concepts in graph theory: the boxicity of a graph, which is the minimum integer k such that a graph can be represented as the intersection graph of some family of axis-parallel k-dimensional boxes, and the existence of hamilton cycles in graphs with minimum degree greater than or equal to the algebraic connectivity. The document also mentions the minimum degree and algebraic connectivity of a graph.
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The minimum integer k such that G can be represented as the intersection graph of some family of axis-parallel k-dimensional boxes is called the boxicity of G.
For every graph with n ≥ 3 vertices and minimum degree δ ≥ n/ 2 has a Hamilton cycle.