“Please don’t throw your cigarette ends on the floor. The cockroaches are getting cancer” is a jocular instruction that has been printed on many signs.  “Please don’t throw cigarette butts on the floor. The cockroaches are getting cancer” was a sign posted in a teen center in 1970. “Please don’t throw cigaret butts on the floor. The cockroaches are getting cancer” was cited in the 1980 book Graffiti in the Big Ten.
         
 
2 December 1970, Bensonville (IL) Register, “Reveal Teen Center Plans” by Judy Mehl, sec. 1, pg. 2, col. 3:
Floors are clean and a sign in his office reads, “Please don’t throw cigarette butts on the floor. The cockroaches are getting cancer.”
 
Google News Archive
24 July 1980, Milwaukee (WI) Journal, “Researchers found this book written on the walls” by Robert W. Wells, Accent sec., pg. 4, col. 1:
“Please don’t throw cigaret butts on the floor. The cockroaches are getting cancer.” 
(The book “Graffiti in the Big Ten.”—ed.)
 
Google Books
Chi Town
By Norbert Blei
Evanston, IL: Northwestern University Press
2003
Pg. 140:
PLEASE DON’T THROW CIGARETTE BUTTS ON THE FLOOR. OUR COCKROACHES ARE GETTING CANCER.
 
Google News Archive
27 July 2005, Hancock (MD) News, “People Told Us…,” pg. 16, col. 3:
SIGN IN PICNIC AREA:
“Please don’t throw cigarette ends on the floor. The cockroaches are getting cancer.”
 
Google Books
Health and Humor
By Charles Frederick Schafer
Pella, IA: The Write Place
2008
Pg. 333:
A sign seen in England: “Please do not throw your cigarette butts on the floor. The cockroaches are getting cancer.”
   
Google Books
The Weak Send Rocks, The Strong Send Rockets:
A Thousand Diplomatic and Un-diplomatic Jokes
By Marek Arnaud
New York, NY: Eloquent Books
2009
Pg. 202:
In an unidentified bar or restaurant:
PLEASE DON’T THROW YOUR CIGARETTES ON THE FLOOR. COCKROACHES ARE GETTING CANCER.
 
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PLEASE… Don’t throw your cigarette end on the floor. The cockroaches are getting cancer.
7:33 AM - 29 Mar 2015