Elementary submodels in infinite combinatorics
Lajos Soukup
TL;DR
This paper explores the application of elementary submodels in infinite combinatorics, providing new proofs and improvements of classical theorems to enhance understanding and simplify complex proofs.
Contribution
It introduces the use of elementary submodels in infinite combinatorics, offering new proofs of classical theorems and improvements on existing decomposition results.
Findings
New proof of Nash-Williams's cycle-decomposition theorem
Improved decomposition theorem of Laviolette on bond-faithful decompositions
Demonstrates the effectiveness of elementary submodels in simplifying proofs
Abstract
The usage of elementary submodels is a simple but powerful method to prove theorems, or to simplify proofs in infinite combinatorics. First we introduce all the necessary concepts of logic, then we prove classical theorems using elementary submodels. We also present a new proof of Nash-Williams's theorem on cycle-decomposition of graphs, and finally we improve a decomposition theorem of Laviolette concerning bond-faithful decompositions of graphs.
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Taxonomy
TopicsAdvanced Graph Theory Research · Constraint Satisfaction and Optimization · Complexity and Algorithms in Graphs