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author:

You, Chunlin (You, Chunlin.) [1] | Lin, Qizhong (Lin, Qizhong.) [2] (Scholars:林启忠) | Chen, Xun (Chen, Xun.) [3]

Indexed by:

SCIE

Abstract:

The book B-n((k)) is the graph consisting of n copies of Kk+1, all sharing a common K-k. A graph H = (W, E-H) is said to have bandwidth at most b if there exists a labeling of W as w(1), w(2),..., w(n) such that vertical bar i - j vertical bar <= b for every edge w(i)w(j) is an element of E-H. We say H = (W , E-H) is a bipartite balanced (beta, Delta) graph if it is a bipartite graph with bandwidth at most beta vertical bar W vertical bar and maximum degree at most Delta, and furthermore it has a proper 2-coloring chi : W -> [2] such that I vertical bar vertical bar chi(-1) (1)vertical bar - vertical bar chi(-1) (2)vertical bar vertical bar <= beta vertical bar chi(-1) (2)vertical bar. In this paper, we prove that for fixed integer k >= 2 and every bipartite balanced (beta, Delta)-graph H on n vertices, the Ramsey number r(B-n((k)), H) <= (k +1 + o(1))n. As a corollary, we have that for fixed k >= 2 and t >= 2, r(B-tn((k)), theta(n,t)) = (k+ 1 + o(1))tn, where theta(n,t) is the graph consisting of t internally disjoint paths of length n all sharing the same endpoints. (C) 2021 Elsevier B.V. All rights reserved.

Keyword:

Book Ramsey number Regularity method Small bandwidth bipartite graph

Community:

  • [ 1 ] [You, Chunlin]Fuzhou Univ, Ctr Discrete Math, Fuzhou 350108, Peoples R China
  • [ 2 ] [Lin, Qizhong]Fuzhou Univ, Ctr Discrete Math, Fuzhou 350108, Peoples R China
  • [ 3 ] [Chen, Xun]Fuzhou Univ, Ctr Discrete Math, Fuzhou 350108, Peoples R China

Reprint 's Address:

  • 陈勋

    [Chen, Xun]Fuzhou Univ, Ctr Discrete Math, Fuzhou 350108, Peoples R China

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Source :

DISCRETE MATHEMATICS

ISSN: 0012-365X

Year: 2021

Issue: 7

Volume: 344

0 . 9 6 1

JCR@2021

0 . 7 0 0

JCR@2023

ESI Discipline: MATHEMATICS;

ESI HC Threshold:36

JCR Journal Grade:3

CAS Journal Grade:4

Cited Count:

WoS CC Cited Count: 0

SCOPUS Cited Count: 2

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 0

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