Strict 2-threshold graphs

Labeling for Vertices in Strict 2-Threshold Graphs

In this paper, we show a labeling scheme for a class of graphs named Strict 2-Threshold that have threshold dimension 2. The labeling scheme characterizes the structural properties of neighborhood of each vertex. As a consequence, variation of a known recognition algorithm by Rossella Petreschi and Andrea Sterbini published in 1995 is presented, where n is the number of nodes, and m is the numb...

Lecture 23: Threshold Phenomena 2 Infinite Graphs

where the subscript x ∼ pmeans each bit of the input x is set to -1 with probability p independently. Last lecture we argued that μp(f) is a nondecreasing function in p. We also defined the function’s critical probability pc as the least p such that μp(f) is at least 1 2 . In fact, in the case of finite domains we showed that μp(f) is increasing from 0 to 1 when p goes from 0 to 1, so pc is the...

Towards Characterizing Strict Outerconfluent Graphs

Recognizing Planar Strict Quasi-Parity Graphs

A graph is a strict-quasi parity (SQP) graph if every induced subgraph that is not a clique contains a pair of vertices with no odd chordless path between them (an``even pair''). We present an O…n 3 † algorithm for recognizing planar strict quasi-parity graphs, based on Wen-Lian Hsu's decomposition of planar (perfect) graphs and on the (non-algorithmic) characterization of planar minimal non-SQ...

Strict Refinement for Direct Sums and Graphs

We study direct sums of structures with a one element subuniverse. We give a characterization of direct sums reminescent to that of inner products of groups. The strict refinement property is adapted to direct sums and to restricted Cartesian products of graphs. If a structure has the strict refinement property (for direct products), it has the strict refinement property for direct sums. Connec...