Claw-freeness, 3-homogeneous subsets of a graph and a reconstruction problem

Details Claw-freeness, 3-homogeneous subsets of a graph and a reconstruction problem Claw-freeness, 3-homogeneous subsets of a graph and a reconstruction problem

2008-12-06

arxiv.org/abs/0812.1278v1

Mathematics

Combinatorics

10 pages, 2 figures

Scientific paper

We describe $Forb\{K_{1,3}, \overline {K_{1,3}}\}$, the class of graphs $G$ such that $G$ and its complement $ \overline{G}$ are claw-free. With few exceptions, it is made of graphs whose connected components consist of cycles of length at least 4, paths or isolated vertices, and of the complements of these graphs. Considering the hypergraph ${\mathcal H} ^{(3)}(G)$ made of the 3-element subsets of the vertex set of a graph $G$ on which $G$ induces a clique or an independent subset, we deduce from above a description of the Boolean sum $G\dot{+}G'$ of two graphs $G$ and $G'$ giving the same hypergraph. We indicate the role of this latter description in a reconstruction problem of graphs up to complementation.

Affiliated with

Also associated with

No associations

Rating

Claw-freeness, 3-homogeneous subsets of a graph and a reconstruction problem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Claw-freeness, 3-homogeneous subsets of a graph and a reconstruction problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Claw-freeness, 3-homogeneous subsets of a graph and a reconstruction problem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-719763