IJPAM: Volume 67, No. 2 (2011)

A REMARK ON THE CHROMATIC POLYNOMIALS OF
INCOMPARABILITY GRAPHS OF POSETS

Yilun ShangRoom 501, No. 30, Lane 192, ZiYe Road, Pudong New Area, Shanghai, P.R. CHINA
Institute for Cyber Security
University of Texas at San Antonio
San Antonio, Texas, 78249, USA
e-mail: shylmath@hotmail.com


Abstract.The incomparability graph $I(P)$, associated with a poset $P$, has vertex set $P$ and edge $ij$ whenever $i$ and $j$ are incomparability in $P$. In this remark we present an identity involving chromatic polynomials of incomparability graphs of a sequence of posets. The result can be regarded as a generalization of a symmetrical Eulerian identity.

Received: December 12, 2010

AMS Subject Classification: 06A07, 05C31

Key Words and Phrases: poset, chromatic polynomial, incomparability graph

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 67
Issue: 2