Trees with an On-Line Degree Ramsey Number of Four
Name
Rolnick-2011-Trees with an on-line.pdf
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728.93 KB
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Adobe PDF
Checksum (MD5)
78160aaaacb91726c9929147f9088e70
Author(s)
Rolnick, David S.
Date Issued
September 2011
Journal
Electronic Journal of Combinatorics
Publisher
Electronic Journal of Combinatorics
Citation
Rolnick, David. "Trees with an On-Line Degree Ramsey Number of Four." Electronic Journal of Combinatorics, Volume 18, Issue 1 (2011).
Version
Final published version
Abstract
On-line Ramsey theory studies a graph-building game between two players. The player called Builder builds edges one at a time, and the player called Painter paints each new edge red or blue after it is built. The graph constructed is called the background graph. Builder's goal is to cause the background graph to contain a monochromatic copy of a given goal graph, and Painter's goal is to prevent this. In the S[subscript k]-game variant of the typical game, the background graph is constrained to have maximum degree no greater than k. The on-line degree Ramsey number [˚over R][subscript Δ](G) of a graph G is the minimum k such that Builder wins an S[subscript k]-game in which G is the goal graph. Butterfield et al. previously determined all graphs G satisfying [˚ over R][subscript Δ](G)≤3. We provide a complete classification of trees T satisfying [˚ over R][subscript Δ](T)=4.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.37236/660
