Packing and covering triangles in \(K_{4}\)-free planar graphs

DOI10.1007/s00373-011-1071-9zbMath1256.05188OpenAlexW2137429845MaRDI QIDQ1926019

Steéphan Thomassé, Alexandr V. Kostochka, Penny E. Haxell

Publication date: 27 December 2012

Published in: Graphs and Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00373-011-1071-9

zbMATH Keywords

planarTuza's conjecturetriangle packing and covering

Mathematics Subject Classification ID

Planar graphs; geometric and topological aspects of graph theory (05C10) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70) Combinatorial aspects of packing and covering (05B40)

Related Items (17)

Recent techniques and results on the Erdős-Pósa property ⋮ Fractional \(K_{4}\)-covers ⋮ Triangle packings and transversals of some \(K_{4}\)-free graphs ⋮ Packing and covering directed triangles ⋮ Total Dual Integrality of Triangle Covering ⋮ Unnamed Item ⋮ Maximal \(k\)-edge-colorable subgraphs, Vizing's theorem, and Tuza's conjecture ⋮ Covering triangles in edge-weighted graphs ⋮ On Tuza's conjecture for triangulations and graphs with small treewidth ⋮ On Tuza's conjecture for triangulations and graphs with small treewidth ⋮ Sufficient Conditions for Tuza’s Conjecture on Packing and Covering Triangles ⋮ Approximation algorithms on \(k\)-cycle transversal and \(k\)-clique transversal ⋮ Packing and covering directed triangles asymptotically ⋮ Unnamed Item ⋮ Triangle packing and covering in dense random graphs ⋮ Characterizing 3-uniform linear extremal hypergraphs on feedback vertex number ⋮ Tuza's conjecture for graphs with maximum average degree less than 7

Cites Work

• Unnamed Item
• A stability theorem on fractional covering of triangles by edges
• Packing and covering triangles in planar graphs
• Packing and covering triangles in graphs
• Packing and covering triangles in tripartite graphs
• On a conjecture of Tuza about packing and covering of triangles
• A conjecture on triangles of graphs
• Some Ramsey-Type Numbers and the Independence Ratio
• Packing Triangles in Weighted Graphs

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