In the Maximum Degree Contraction problem, input is a graph G on n vertices, and integers k, d, objective to check whether can be transformed into of maximum degree at most using k edge contractions. A simple brute-force algorithm that checks all possible sets edges for solution runs in time $$n^{\mathcal {O}(k)}$$ . As our first result, we prove this asymptotically optimal, upto constants expo...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 26 February 2020Accepted: 15 March 2021Published online: 01 June 2021Keywordsindependence number, bounded maximum degree, bipartite extremal problemsAMS Subject Headings05C35, 05D40Publication DataISSN (print): 0895-4801ISSN (online): 1095-7146Publisher: Society for Indus...

We study the maximum likelihood (ML) degree of linear concentration models in algebraic statistics. relate it to an intersection problem on variety complete quadrics. This allows us pr...

The reconfiguration graph R k ( G ) for the -colorings of a has as vertex set all possible and two colorings are adjacent if they differ in color exactly one . Let d , ? 1 be integers such that + We prove every ? > 0 with n vertices maximum average degree ? diameter O log ? This significantly strengthens several existing results.