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  • Online publication date: March 2017

Reverse mathematics and graph coloring: eliminating diagonalization

[1] Dwight R., Bean, Effective coloration,The Journal of Symbolic Logic, vol. 41 (1976), pp. 469–480.
[2] S., Felsner, On-line chain partitions of orders,Theoretical Computer Science, vol. 175 (1997), pp. 283–292.
[3] William, Gasarch and Jeffry L., Hirst, Reverse mathematics and recursive graph theory,Mathematical Logic Quarterly, vol. 44 (1998), pp. 465–473.
[4] A., Gyárfás and J., Lehel, On-line and first-fit colorings of graphs,Journal of Graph Theory, vol. 12 (1988), pp. 217–227.
[5] A., Gyárfás and J., Lehel, First-fit and on-line chromatic number of families of graphs,Ars Combinatoria, vol. 29C (1990), pp. 168–176.
[6] Carl G., Jockusch, Jr., Degrees of functions with no fixed points,Logic, methodology and philosophy of science, VIII (Moscow, 1987) (J. E., Fenstad, I.T., Frolov, and R., Hilpinen, editors), North-Holland, Amsterdam, 1989, pp. 191–201.
[7] H. A., Kierstead, An effective version of Dilworth's theorem,Transactions of the American Mathematical Society, vol. 268 (1981), pp. 63–77.
[8] H. A., Kierstead, Recursive and on-line graph coloring,Handbook of recursive mathematics, vol. 2, North-Holland, Amsterdam, 1988, pp. 1233–1269.
[9] H. A., Kierstead, Coloring graphs on-line,Online algorithms (Schloss Dagstuhl, 1996), Lecture Notes in Computer Science, vol. 1442, Springer, Berlin, 1998, pp. 281–305.
[10] H. A., Kierstead, S. G., Penrice, and W. T., Trotter, On-line graph coloring and recursive graph theory,SIAMJournal on DiscreteMathematics, vol. 7 (1994), pp. 72–89.
[11] H. A., Kierstead, First-fit and on-line coloring of graphs which do not induce P 5, SIAM Journal on Discrete Mathematics, vol. 8 (1995), pp. 485–498.
[12] H. A., Kierstead and W. T., Trotter, An extremal problem in recursive combinatorics,Congressus Numerantium, vol. 33 (1981), pp. 143–153.
[13] L., Lovász, On the decomposition of graphs,Studia Scientiarum Mathematicarum Hungarica, vol. 1 (1966), pp. 237–238.
[14] Alfred B., Manaster and Joseph G., Rosenstein, Effective matchmaking (recursion theoretic aspects of a theorem of Philip Hall),Proceedings of the London Mathematical Society. Third Series, vol. 25 (1972), pp. 615–654.
[15] Alfred B., Manaster and Joseph G., Rosenstein, Effective matchmaking and k-chromatic graphs, Proceedings of the American Mathematical Society, vol. 39 (1973), pp. 371–378.
[16] James H., Schmerl, Recursive colorings of graphs,Canadian Journal of Mathematics, vol. 32 (1980), pp. 821–830.
[17] James H., Schmerl, Graph coloring and reverse mathematics,Mathematical Logic Quarterly, vol. 46 (2000), pp. 543–548.
[18] Stephen G., Simpson, Subsystems of second order arithmetic, Perspectives inMathematical Logic, Springer-Verlag, 1998.