@article{6325cc7028f14f1dbe24affbc6409d7f,

title = "Separation dimension of bounded degree graphs",

abstract = "The separation dimension of a graph G is the smallest natural number k for which the vertices of G can be embedded in Rk such that any pair of disjoint edges in G can be separated by a hyperplane normal to one of the axes. Equivalently, it is the smallest possible cardinality of a family F of total orders of the vertices of G such that for any two disjoint edges of G, there exists at least one total order in F in which all the vertices in one edge precede those in the other. In general, the maximum separation dimension of a graph on n vertices is Θ(log n). In this article, we focus on bounded degree graphs and show that the separation dimension of a graph with maximum degree d is at most 29 log ∗ d d. We also demonstrate that the above bound is nearly tight by showing that, for every d, almost all d-regular graphs have separation dimension at least ⌈d/2⌉.",

keywords = "Bounded degree, Boxicity, Linegraph, Separation dimension",

author = "Noga Alon and Manu Basavaraju and Chandran, {L. Sunil} and Rogers Mathew and Deepak Rajendraprasad",

note = "Publisher Copyright: {\textcopyright} 2015 Society for Industrial and Applied Mathematics.",

year = "2015",

doi = "10.1137/140973013",

language = "אנגלית",

volume = "29",

pages = "59--64",

journal = "SIAM Journal on Discrete Mathematics",

issn = "0895-4801",

publisher = "Society for Industrial and Applied Mathematics (SIAM)",

number = "1",

}