Tuza’s Conjecture for graphs with maximum average degree less than 7

Aparna Lakshmanan, 2012, Small edge sets meeting all triangles of a graph, Graphs Combin., 28, 381, 10.1007/s00373-011-1048-8

S. Aparna Lakshmanan, Cs. Bujtás, Zs. Tuza, Induced cycles in triangle graphs, 2014 (submitted for publication). arXiv:1410.8807.

Chapuy, 2014, Packing triangles in weighted graphs, SIAM J. Discrete Math., 28, 226, 10.1137/100803869

Deming, 1979, Independence numbers of graphs—an extension of the Koenig–Egervary theorem, Discrete Math., 27, 23, 10.1016/0012-365X(79)90066-9

Diestel, 2010, vol. 173

Egerváry, 1931, On combinatorial properties of matrices, Mat. Lapok, 38, 16

Haxell, 1999, Packing and covering triangles in graphs, Discrete Math., 195, 251, 10.1016/S0012-365X(98)00183-6

Haxell, 2012, A stability theorem on fractional covering of triangles by edges, European J. Combin., 33, 799, 10.1016/j.ejc.2011.09.024

Haxell, 2012, Packing and covering triangles in K4-free planar graphs, Graphs Combin., 28, 653, 10.1007/s00373-011-1071-9

Haxell, 2001, Integer and fractional packings in dense graphs, Combinatorica, 21, 13, 10.1007/s004930170003

Hsu, 1981, A polynomial algorithm for maximum weighted vertex packings on graphs without long odd cycles, Math. Program., 20, 225, 10.1007/BF01589347

Kayll, 2010, König–Egerváry graphs are non-Edmonds, Graphs Combin., 26, 721, 10.1007/s00373-010-0940-y

König, 1931, Graphen und matrizen, Mat. Lapok, 38, 116

Krivelevich, 1995, On a conjecture of Tuza about packing and covering of triangles, Discrete Math., 142, 281, 10.1016/0012-365X(93)00228-W

Mader, 1998, 3n−5 edges do force a subdivision of K5, Combinatorica, 18, 569, 10.1007/s004930050041

B.D. McKay, A. Piperno, Nauty User’s Guide (Version 2.5), 2013. URL: http://cs.anu.edu.au/~bdm/nauty/.

Thomas, 1999, Recent excluded minor theorems for graphs, vol. 267, 201

Tuza, 1984, Finite and infinite sets. Vol. I, II, vol. 37, 888

Tuza, 1990, A conjecture on triangles of graphs, Graphs Combin., 6, 373, 10.1007/BF01787705

Wagner, 1937, Über eine Eigenschaft der ebenen Komplexe, Math. Ann., 114, 570, 10.1007/BF01594196

D.W. Cranston, D.B. West, A guide to discharging (submitted for publication). arXiv:1306.4434.

Yuster, 2012, Dense graphs with a large triangle cover have a large triangle packing, Combin. Probab. Comput., 21, 952, 10.1017/S0963548312000235