Tuza's Conjecture for Graphs of Maximum Average Degree Less Than 7
Combinatorics
2015-04-14 v3
Abstract
Tuza's Conjecture states that if a graph does not contain more than edge-disjoint triangles, then some set of at most edges meets all triangles of . We prove Tuza's Conjecture for all graphs having no subgraph with average degree at least . As a key tool in the proof, we introduce a notion of reducible sets for Tuza's Conjecture; these are substructures which cannot occur in a minimal counterexample to Tuza's Conjecture. We also introduce weak K\"onig--Egerv\'ary graphs, a generalization of the well-studied K\"onig--Egerv\'ary graphs.
Keywords
Cite
@article{arxiv.1308.2211,
title = {Tuza's Conjecture for Graphs of Maximum Average Degree Less Than 7},
author = {Gregory J. Puleo},
journal= {arXiv preprint arXiv:1308.2211},
year = {2015}
}
Comments
26 pages, 11 figures. Updated with journal reference and some revisions (corrected a few minor errors, added some more background material)