# Landon Rabern

**Landon W. Rabern**,

an American mathematician and software engineer in the AI industry. His research interests include combinatorics and graph theory, such as clique problems, graph coloring and edge coloring.
He holds a B.Sc. from Washington University in St. Louis in 2003,
a M.Sc. from University of California, Santa Barbara in 2005, and
a Ph.D. from Arizona State University in 2013.
As a computer chess programmer, Landon Rabern is author the WinBoard compatible chess engine Betsy ^{[1]}, which was the first published chess engine able to play Chess960 ^{[2]}.

## Contents

# Selected Publications

^{[3]}

## 2003

- Landon W. Rabern (
**2003**).*Properties of Magic Squares of Squares*. Rose-Hulman Undergraduate Mathematics Journal, Vol. 4, No. 1

## 2005 ...

- Landon Rabern (
**2005**).*Some bounds on convex combinations of ω and χ for decompositions into many parts*. arXiv:math/0512291 - Landon Rabern (
**2006**).*New upper bounds on the chromatic number of a graph*. arXiv:math/0606632 - Landon Rabern (
**2006**).*On Graph Associations*. SIAM Journal on Discrete Mathematics, Vol. 20, No. 2 - Landon Rabern (
**2007**).*The Borodin-Kostochka Conjecture for Graphs Containing a Doubly Critical Edge*. Electronic Journal of Combinatorics, Vol. 14 - Landon Rabern (
**2008**).*A Note On Reed's Conjecture*. SIAM Journal on Discrete Mathematics, Vol. 22, No. 2^{[4]} - Brian Rabern, Landon Rabern (
**2008**).*A simple solution to the hardest logic puzzle ever*. Analysis, Vol. 68, No. 2^{[5]} - Landon Rabern (
**2009**).*On hitting all maximum cliques with an independent set*. arXiv:0907.3705

## 2010 ...

- Landon Rabern (
**2011**).*An improvement on Brooks' Theorem*. arXiv:1102.1021^{[6]} - Landon Rabern (
**2011**).*A note on vertex partitions*. arXiv:1107.1735 - Landon Rabern (
**2012**).*Partitioning and coloring with degree constraints*. arXiv:1202.5855 - Landon Rabern (
**2012**).*A different short proof of Brooks' theorem*. arXiv:1205.3253 - Landon Rabern (
**2012**).*Coloring graphs with dense neighborhoods*. arXiv:1209.3646 - Landon Rabern (
**2013**).*Coloring graphs from almost maximum degree sized palettes*. Ph.D. thesis, Arizona State University, advisor: Henry A. Kierstead, pdf - Daniel W. Cranston, Landon Rabern (
**2014**).*Brooks' Theorem and Beyond*. arXiv:1403.0479 - Hal Kierstead, Landon Rabern (
**2014**).*Improved lower bounds on the number of edges in list critical and online list critical graphs*. arXiv:1406.7355 - Landon Rabern (
**2014**).*A game generalizing Hall’s Theorem*. Discrete Mathematics, Vol. 320^{[7]}

## 2015 ...

- Daniel W. Cranston, Landon Rabern (
**2015**).*Subcubic edge chromatic critical graphs have many edges*. arXiv:1506.04225 - Daniel W. Cranston, Landon Rabern (
**2015**).*Edge-coloring via fixable subgraphs*. arXiv:1507.05600 - Daniel W. Cranston, Landon Rabern (
**2015**).*Beyond Degree Choosability*. arXiv:1511.00350 - Hal Kierstead, Landon Rabern (
**2015**).*Extracting list colorings from large independent sets*. arXiv:1512.08130 - Landon Rabern (
**2016**).*A better lower bound on average degree of 4-list-critical graphs*. arXiv:1602.08532 - Landon Rabern (
**2016**).*A better lower bound on average degree of k-list-critical graphs*. arXiv:1608.06989 - Daniel W. Cranston, Landon Rabern (
**2018**).*Planar graphs are 9/2-colorable*. Journal of Combinatorial Theory, Series B, Vol. 133, arXiv:1410.7233 - Daniel W. Cranston, Landon Rabern (
**2019**).*The Hilton--Zhao Conjecture is True for Graphs with Maximum Degree 4*. SIAM Journal on Discrete Mathematics, Vol. 33, No. 3, arXiv:1703.00959

# Forum Posts

- Re: C or C++ for Chess Programming? by Landon Rabern, CCC, August 18, 2000
- Betsy 5.0 is now winboard compatable by Landon Rabern, CCC, September 06, 2000
- Betsy 5.26 by Landon Rabern, CCC, July 06, 2001
- Re: FRC_TheBaron_101 Vs Fritz8 (Castling vs Not Castling rules) by Landon Rabern, CCC, June 24, 2003

# External Links

- landon rabern
- landon rabern | LinkedIn
- landon rabern - Google Scholar Citations
- Landon Rabern - The Mathematics Genealogy Project
- landon (landon rabern) · GitHub
- GitHub - landon/Chess: Beginnings of a port of Betsy to C#

# References

- ↑ landon_resume.pdf
- ↑ Der Chess960-Express ist nicht mehr aufzuhalten, Chess Tigers Training Center, July 20, 2005 (German)
- ↑ dblp: Landon Rabern
- ↑ Chvátal graph from Wikipedia
- ↑ George Boolos credits Raymond Smullyan as the originator of the puzzle and John McCarthy with adding the difficulty of not knowing what
**da**and**ja**mean, George Boolos (**1996**).*The Hardest Logic Puzzle Ever*. The Harvard Review of Philosophy, Vol. 6, No. 1, The Hardest Logic Puzzle Ever - Wikipedia - ↑ Brooks' theorem from Wikipedia
- ↑ Hall's marriage theorem - Wikipedia