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Extremal bipartite independence number and balanced coloring
[article]
2022
arXiv
pre-print
In this paper, we establish a couple of results on extremal problems in bipartite graphs. Firstly, we show that every sufficiently large bipartite graph with average degree Δ and with n vertices on each side has a balanced independent set containing (1-ϵ) logΔ/Δ n vertices from each side for small ϵ > 0. Secondly, we prove that the vertex set of every sufficiently large balanced bipartite graph with maximum degree at most Δ can be partitioned into (1+ϵ)Δ/logΔ balanced independent sets. Both of
arXiv:2107.02506v2
fatcat:g5zwnkhucbeyhkiz4u4mskzliy