Tuza conjectured that if a simple graph G does not contain more than k pairwise edge-disjoint triangles, then there exists a set of at most 2k edges that meets all triangles in G. It has been shown that this conjecture is true for planar graphs and the bound is sharp. In this paper, we characterize the set of extremal planar graphs.
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Haxell P.E.: Packing and covering triangles in graphs. Discrete Math. 195, 251–254 (1999)
Haxell P.E., Kohayakawa Y.: Packing and covering triangles in tripartite graphs. Graphs Combin. 14, 1–10 (1998)
Krivelevich M.: On a conjecture of Tuza about packing and covering of triangles. Discrete Math. 142, 281–286 (1995)
Tuza, Zs.: Conjecture, Finite and Infinite Sets (Eger, Hungary 1981). In: Hajnal, A., Lovász, L., Sós, V. T. (eds.) Proc. Colloq. Math. Soc. J. Bolyai, vol. 37, p. 888. North-Holland, Amsterdam (1984)
Tuza Zs.: A conjecture on triangles of graphs. Graphs Combin. 6, 373–380 (1990)
Q. Cui was partially supported by Jiangsu Planned Projects for Postdoctoral Research Funds, P. Haxell was partially supported by NSERC and W. Ma was partially supported by an NSERC Undergraduate Student Research Assistantship.
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Cui, Q., Haxell, P. & Ma, W. Packing and Covering Triangles in Planar Graphs. Graphs and Combinatorics 25, 817–824 (2009). https://doi.org/10.1007/s00373-010-0881-5
- Packing and covering
- Planar graph
Mathematics Subject Classification (2000)