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Title: The size Ramsey number of short subdivisions of bounded degree graphs
Abstract

For graphsGandF, writeif any coloring of the edges ofGwithcolors yields a monochromatic copy of the graphF. Supposeis obtained from a graphSwithsvertices and maximum degreedby subdividing its edgeshtimes (that is, by replacing the edges ofSby paths of lengthh + 1). We prove that there exists a graphGwith no more thanedges for whichholds, provided that. We also extend this result to the case in whichQis a graph with maximum degreedonqvertices with the property that every pair of vertices of degree greater than 2 are distance at leasth + 1 apart. This complements work of Pak regarding the size Ramsey number of “long subdivisions” of bounded degree graphs.

 
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NSF-PAR ID:
10064220
Author(s) / Creator(s):
 ;  ;  
Publisher / Repository:
Wiley Blackwell (John Wiley & Sons)
Date Published:
Journal Name:
Random Structures & Algorithms
Volume:
54
Issue:
2
ISSN:
1042-9832
Page Range / eLocation ID:
p. 304-339
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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