A Structural Approach for Independent Domination of Regular Graphs

We consider bounds on the minimum cardinality of an independent dominating set in regular graphs with large degree (linear in the number of vertices). Better bounds are obtained for various ranges of the degree. This is done by working with a variant of the clique graph of the complement.

[1]  Julie Haviland.  Upper bounds for independent domination in regular graphs , 2007, Discret. Math..

[2]  C. Payan.  Coverings by minimal transversals , 1978, Discret. Math..

[3]  M. Rosenfeld.  Independent sets in regular graphs , 1964 .

[4]  E. S. Wolk.  The comparability graph of a tree , 1962 .

[5]  William Duckworth,et al.  Linear Programming and the Worst-Case Analysis of Greedy Algorithms on Cubic Graphs , 2010, Electron. J. Comb..

[6]  Paul Erdös,et al.  Disjoint cliques and disjoint maximal independent sets of vertices in graphs , 1982, Discret. Math..

[7]  Landon Rabern,et al.  On hitting all maximum cliques with an independent set , 2009, J. Graph Theory.

[8]  Stephen T. Hedetniemi,et al.  Disjoint independent dominating sets in graphs , 1976, Discret. Math..

[9]  Wayne Goddard,et al.  On the Independent Domination Number of Regular Graphs , 2012 .

[10]  E. S. Wolk.  A note on “The comparability graph of a tree” , 1965 .

[11]  Michele Zito,et al.  Greedy Algorithms for Minimisation Problems in Random Regular Graphs , 2001, ESA.

[12]  Alexandr V. Kostochka,et al.  The independent domination number of a cubic 3-connected graph can be much larger than its domination number , 1993, Graphs Comb..

[13]  J. A. Bondy,et al.  Graph Theory with Applications , 1978 .

[14]  William Duckworth,et al.  On the Independent Domination Number of Random Regular Graphs , 2006, Combinatorics, Probability and Computing.

[15]  Julie Haviland.  Independent dominating sets in regular graphs , 2013, J. Comb. Optim..

[16]  Odile Favaron,et al.  Two relations between the parameters of independence and irredundance , 1988, Discret. Math..