Add to ORKGWe show that every simple planar near-triangulation with minimum degree at least three contains two disjoint total dominating sets. The class includes all simple planar triangulations other than the triangle. This affirms a conjecture of Goddard and Henning [Thoroughly dispersed colorings, J. Graph Theory, 88 (2018) 174-191]
summary:A dominating set in a graph $G$ is a connected dominating set of $G$ if it induces a connect...
AbstractLet G be a planar graph with maximum degree Δ≥7 and without adjacent 4-cycles, that is, two ...
We show that every triconnected planar graph of maximum degree five is subhamiltonian planar. A grap...
A total dominating set of a graph is a subset of such that every vertex in is adjacent to at least o...
A dominating set of a graph $G$ is a subset $D$ of vertices such that every vertex not in $D$ is adj...
AbstractIn 1996, Matheson and Tarjan conjectured that any n-vertex plane triangulation with n suffic...
AbstractMotivated by an application to unstructured multigrid calculations, we consider the problem ...
AbstractMacGillivary and Seyffarth [G. MacGillivray, K. Seyffarth, Domination numbers of planar grap...
An annulus triangulation G is a 2-connected plane graph with two disjoint faces f1 and f2 such that ...
Motivated by an application to unstructured multigrid calculations, we consider the problem of asymp...
AbstractLet G be a planar graph with maximum degree Δ≥7 and without intersecting 3-cycles; that is, ...
213–229) proved that planar graphs of diameter three have domination number at most ten. Recently it...
A planar graph G = (V,E) is a graph that can be embedded in the plane, i.e. it can be drawn in the p...
AbstractLet G be a planar graph without adjacent 3-cycles, that is, two cycles of length 3 are not i...
A recent result of Henning and Southey (A note on graphs with disjoint dominating and total dominati...
summary:A dominating set in a graph $G$ is a connected dominating set of $G$ if it induces a connect...
AbstractLet G be a planar graph with maximum degree Δ≥7 and without adjacent 4-cycles, that is, two ...
We show that every triconnected planar graph of maximum degree five is subhamiltonian planar. A grap...
A total dominating set of a graph is a subset of such that every vertex in is adjacent to at least o...
A dominating set of a graph $G$ is a subset $D$ of vertices such that every vertex not in $D$ is adj...
AbstractIn 1996, Matheson and Tarjan conjectured that any n-vertex plane triangulation with n suffic...
AbstractMotivated by an application to unstructured multigrid calculations, we consider the problem ...
AbstractMacGillivary and Seyffarth [G. MacGillivray, K. Seyffarth, Domination numbers of planar grap...
An annulus triangulation G is a 2-connected plane graph with two disjoint faces f1 and f2 such that ...
Motivated by an application to unstructured multigrid calculations, we consider the problem of asymp...
AbstractLet G be a planar graph with maximum degree Δ≥7 and without intersecting 3-cycles; that is, ...
213–229) proved that planar graphs of diameter three have domination number at most ten. Recently it...
A planar graph G = (V,E) is a graph that can be embedded in the plane, i.e. it can be drawn in the p...
AbstractLet G be a planar graph without adjacent 3-cycles, that is, two cycles of length 3 are not i...
A recent result of Henning and Southey (A note on graphs with disjoint dominating and total dominati...
summary:A dominating set in a graph $G$ is a connected dominating set of $G$ if it induces a connect...
AbstractLet G be a planar graph with maximum degree Δ≥7 and without adjacent 4-cycles, that is, two ...
We show that every triconnected planar graph of maximum degree five is subhamiltonian planar. A grap...