Packing and Covering Triangles in K 4-free Planar Graphs

@article{Haxell2012PackingAC,
title={Packing and Covering Triangles in K 4-free Planar Graphs},
author={Penny E. Haxell and Alexandr V. Kostochka and St{\'e}phan Thomass{\'e}},
journal={Graphs and Combinatorics},
year={2012},
volume={28},
pages={653-662}
}

We show that every K4-free planar graph with at most ν edge-disjoint triangles contains a set of at most 32ν edges whose removal makes the graph triangle-free. Moreover, equality is attained only when G is the edge-disjoint union of 5-wheels plus possibly some edges that are not in triangles. We also show that the same statement is true if instead of planar graphs we consider the class of graphs in which each edge belongs to at most two triangles. In contrast, it is known that for any c < 2… CONTINUE READING