Graphs whose every independent set has a common neighbour

Every Body Has a Brain

[1] http://ebhb.morphonix.com/ [2] http://fireflyfoundation.wordpress.com/brain-games/every-body-has-a-brain/ [3] http://dev.cdgr.ucsb.edu/organizations/morphonix [4] http://dev.cdgr.ucsb.edu/category/genre/educational [5] http://dev.cdgr.ucsb.edu/category/genre/music/dance [6] http://dev.cdgr.ucsb.edu/category/topics/anatomy [7] http://dev.cdgr.ucsb.edu/category/topics/brain [8] http://dev.cdg...

Every Algorithm Has a POV

Graphs whose edge set can be partitioned into maximum matchings

This article provides structural characterization of simple graphs whose edge-set can be partitioned into maximum matchings. We use Vizing’s classification of simple graphs based on edge chromatic index.

Independent domination in directed graphs

In this paper we initialize the study of independent domination in directed graphs. We show that an independent dominating set of an orientation of a graph is also an independent dominating set of the underlying graph, but that the converse is not true in general. We then prove existence and uniqueness theorems for several classes of digraphs including orientations of complete graphs, paths, tr...

Approximating independent set in perturbed graphs

For the maximum independent set problem, strong inapproximability bounds for worst-case efficient algorithms exist. We give a deterministic algorithm beating these bounds, with polynomial expected running-time for semi-random graphs: An adversary chooses a graph with n vertices, and then edges are flipped with a probability of ε. Our algorithm guarantees an approximation ratio of O( √ nε) for s...