Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6871136 | Discrete Applied Mathematics | 2018 | 5 Pages |
Abstract
A crown graph (also known as a cocktail party graph) Hn,n is a graph obtained from the complete bipartite graph Kn,n by removing a perfect matching. In this paper, we show that for nâ¥5, Hn,n's representation number is ânâ2â. This result not only provides a complete solution to the open Problem 7.4.2 in Kitaev and Lozin (2015), but also gives a negative answer to the question raised in Problem 7.2.7 in Kitaev and Lozin (2015) on 3-word-representability of bipartite graphs. As a byproduct, we obtain a new example of a graph class with a high representation number.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Marc Glen, Sergey Kitaev, Artem Pyatkin,