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math.CO2022
On Proper Colorings of Functions
Tamás Csernák
We investigate the infinite version of the -switch problem of Greenwell and Lovász. Given infinite cardinals and , for functions we say that they are total…
math.CO2022
List Chromatic Number of Finitary Matroids: A Generalization of Seymour's Result
Tamás Csernák
Seymour proved that the chromatic numbers and the list chromatic numbers of loop-free finite matroids are the same. In this paper we prove the same statement for infinite, loop-fre…
math.LO2022
Infinite Combinatorics revisited in the absence of Axiom of Choice
Tamás Csernák, Lajos Soukup
We investigate the provability of classical combinatorial theorems in ZF. Using combinatorial arguments, we establish the following results for each infinite cardinal , (1…