Unavoidable Induced Subgraph of Infinite 2-connected Graphs
Sarah Allred, Guoli Ding, Bogdan Oporowski
TL;DR
This paper extends classical results in infinite graph theory to 2-connected graphs, showing that such graphs necessarily contain certain large induced subgraphs, like rays or vertices of infinite degree.
Contribution
It establishes the 2-connected analogs of Ramsey's and K"{o}nig's theorems for infinite graphs, identifying unavoidable induced subgraphs.
Findings
Every infinite 2-connected graph contains either a ray or a vertex of infinite degree.
The results generalize classical theorems to the 2-connected case.
Provides new structural insights into infinite 2-connected graphs.
Abstract
In 1930, Ramsey proved that every infinite graph contains either an infinite clique or an infinite independent set as an induced subgraph. K\"{o}nig proved that every infinite graph contains either a ray or a vertex of infinite degree. In this paper, we establish the 2-connected analog of these results.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Limits and Structures in Graph Theory · Advanced Graph Theory Research