Journal Title
Title of Journal: Graphs and Combinatorics
|
Abbravation: Graphs and Combinatorics
|
|
|
|
|
|
|
|
Authors: Lei Cheng Jianfeng Hou Yusheng Li Qizhong Lin
Publish Date: 2016/08/04
Volume: 32, Issue: 6, Pages: 2275-2293
Abstract
Given integers kge 2 n ge 2 m ge 2 and a 1a 2ldots a m in mathbb Zbackslash 0 and let fz= sum j=0nc jzj be a polynomial of integer coefficients with c n0 and sum i=1ma ifz for some integer z For a kcoloring of N=12ldots N we say that there is a monochromatic solution of the equation a 1x 1+a 2x 2+cdots +a mx m=fz if there exist pairwise distinct x 1x 2ldots x min N all of the same color such that the equation holds for some zin mathbb Z Problems of this type are often referred to as Ramseytype problems In this paper it is shown that if a i0 for 1le ile m then there exists an integer N 0=Nkmn such that for Nge N 0 each kcoloring of N contains a monochromatic solution x 1x 2ldots x m of the equation a 1x 1+a 2x 2+ cdots +a mx m= fz Moreover if n is odd and there are a i and a j such that a ia j0 for some 1 le ine jle m then the assertion holds similarly
Keywords:
.
|
Other Papers In This Journal:
|