6 papers
Total isolation game in graphs
Michael A. Henning, Douglas F. Rall
The total isolation game is played on a graph by two players who take turns playing a vertex such that if is the set of already played vertices, then a vertex can be select…
On maximizing private neighbors in graphs
Stephen T. Hedetniemi, Douglas F. Rall
Given a set of vertices in a graph , a {\it private neighbor with respect to the set } is any vertex having precisely one neighbor, say ,…
Isolation number: Cartesian and lexicographic products and generalized SierpiÅski graphs
Bostjan Bresar, Tanja Dravec, Daniel P. Johnston +3
The isolation number of a graph is the minimum cardinality of a set such that the subgraph induced by the vertices that are not in the union of the clos…
The domatic number game played on graphs
Bert L. Hartnell, Douglas F. Rall
The domatic number of a graph is the maximum number of pairwise disjoint dominating sets admitted by the graph. We introduce a game based around this graph invariant. The domatic n…
Claw-free cubic graphs are -colorable
Boštjan Brešar, Kirsti Kuenzel, Douglas F. Rall
A -coloring of a graph is a partition of its vertex set into four sets two of which are independent and the other two are -packings. In this paper, we prove that ever…
Isolation game on graphs
Boštjan Brešar, Tanja Dravec, Daniel P. Johnston +2
Given a graph and a family of graphs , an -isolating set, as introduced by Caro and Hansberg, is any set such that contains no member…