
Tuza's Conjecture for Threshold Graphs
Tuza famously conjectured in 1981 that in a graph without k+1 edgedisjo...
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On the treewidth of Hanoi graphs
The objective of the wellknown Towers of Hanoi puzzle is to move a set ...
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Planar Drawings with Few Slopes of Halin Graphs and Nested Pseudotrees
The planar slope number psn(G) of a planar graph G is the minimum number...
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Multitransversals for Triangles and the Tuza's Conjecture
In this paper, we study a primal and dual relationship about triangles: ...
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An Effective Upperbound on Treewidth Using Partial Fillin of Separators
Partitioning a graph using graph separators, and particularly clique sep...
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Glauber dynamics for colourings of chordal graphs and graphs of bounded treewidth
The Glauber dynamics on the colourings of a graph is a random process wh...
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Constant Congestion Brambles
A bramble in an undirected graph G is a family of connected subgraphs of...
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On Tuza's conjecture for triangulations and graphs with small treewidth
Tuza (1981) conjectured that the size τ(G) of a minimum set of edges that intersects every triangle of a graph G is at most twice the size ν(G) of a maximum set of edgedisjoint triangles of G. In this paper we present three results regarding Tuza's Conjecture. We verify it for graphs with treewidth at most 6; we show that τ(G)≤3/2 ν(G) for every planar triangulation G different from K_4; and that τ(G)≤9/5 ν(G) + 1/5 if G is a maximal graph with treewidth 3.
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