The immersion relation is a partial ordering relation on graphs that is weaker than the topological minor relation in the sense that if a graph G contains a graph H as a topological minor, then it also contains it as an immersion but not vice versa. Kuratowski graphs, namely K5 and K3,3, give a precise characterization of planar graphs when excluded as topological minors. In this note we give a...

We study max-cut in classes of graphs defined by forbidding a single graph as a subgraph, induced subgraph, or minor. For the first two containment relations, we prove dichotomy theorems. For the minor order, we show how to solve max-cut in polynomial time for the class obtained by forbidding a graph with crossing number at most one (this generalizes a known result for K5-minor-free graphs) and...

a survey between falsehood and forbiddance seyyed mohammad reza ayati [1] hooshang golmohammadi [2]   abstract one the important issues of jurisprudence is the issue of withholding judgment and religious restraining order. therefore, each of these orders are of different types. studying these orders and their types and also answering the question of what task these withholding judgment and reli...

Michael Schmuker " All models are wrong, but some models are useful. " – George E. P. Box (1979)

Growing powers to manipulate human bodies and minds, not merely to heal disease but to satisfy desires, control deviant behavior, and to change human nature, make urgent questions of whether and how to regulate their use, not merely to assure safety and efficacy but also to safeguard our humanity. Oversight in democratic societies rightly belongs to the polity, not merely to self-appointed expe...

Let 2 ≤ q ≤ min{p, t − 1} be fixed and n → ∞. Suppose that F is a p-uniform hypergraph on n vertices that contains no complete q-uniform hypergraph on t vertices as a trace. We determine the asymptotic maximum size of F in many cases. For example, when q = 2 and p ∈ {t, t+ 1}, the maximum is ( n t−1 ) t−1 + o(nt−1), and when p = t = 3, it is b (n−1) 2 4 c for all n ≥ 3. Our proofs use the Krusk...

We consider binary pairwise graphical models and provide an exact characterization (necessary and sufficient conditions observing signs of potentials) of tightness for the LP relaxation on the triplet-consistent polytope of the MAP inference problem, by forbidding an odd-K5 (complete graph on 5 variables with all edges repulsive) as a signed minor in the signed suspension graph. This captures s...