Graphs without large $K_{2,n}$-minors

Guoli Ding

Graphs without large $K_{2,n}$-minors

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arxiv 1702.01355 v1 pith:RFRIEAUJ submitted 2017-02-05 math.CO

Guoli Ding This is my paper · ORCID

classification math.CO

keywords largeconnectedeverygraphsufficientlydegreegraphsminor

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abstract

The purpose of this paper is to characterize graphs that do not have a large $K_{2,n}$-minor. As corollaries, it is proved that, for any given positive integer $n$, every sufficiently large 3-connected graph with minimum degree at least six, every 4-connected graph with a vertex of sufficiently high degree, and every sufficiently large 5-connected graph must have a $K_{2,n}$-minor.

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Totally $\Delta$-modular IPs with two non-zeros in most rows
cs.DS 2024-11 conditional novelty 7.0 of 10

For fixed Δ and fixed k, every integer program on a totally Δ-modular matrix with at most two non-zero entries per row outside k extra rows and columns can be solved in strongly polynomial time.

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