Separation dimension of a hypergraph H, denoted by π( H) , is the smallest natural number k so that the vertices of H can be embedded in Rk such that any two disjoint edges of H can be separated by a hyperplane normal to one of the axes. We show that the separation dimension of a hypergraph H is equal to the boxicity of the line graph of H. This connection helps us in borrowing results and techniques from the extensive literature on boxicity to study the concept of separation dimension. In this paper, we study the separation dimension of hypergraphs and graphs.
|Number of pages||18|
|State||Published - 1 May 2016|
Bibliographical noteFunding Information:
Deepak Rajendraprasad: Supported by VATAT Postdoctoral Fellowship, Council of Higher Education, Israel and The Israel Science Foundation (Grant Number 862/10).
Rogers Mathew: Supported by VATAT Postdoctoral Fellowship, Council of Higher Education, Israel. This work was done when the author was affiliated with the Department of Computer Science, Caesarea Rothschild Institute, University of Haifa, 31905 Haifa, Israel.
© 2015, Springer Science+Business Media New York.
- Acyclic chromatic number
- Line graph
- Scrambling permutation
- Separation dimension
ASJC Scopus subject areas
- Computer Science (all)
- Computer Science Applications
- Applied Mathematics