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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.
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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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