Given a set F of graphs, a graph G is F-free if G does not contain any member of F as an induced subgraph. Barrus, Kumbhat, and Hartke [4] called F a degree-sequence-forcing (DSF) set if, for each graph G in the class C of F-free graphs, every realization of the degree sequence of G is also in C. A DSF set is minimal if no proper subset is also DSF. In this paper, we present new properties of m...

Subshifts are shift invariant closed subsets of Σ d , minimal subshifts are subshifts in which all points contain the same patterns. It has been proved by Jeandel and Vanier that the Turing degree spectra of nonperiodic minimal subshifts always contain the cone of Turing degrees above any of its degree. It was however not known whether each minimal subshift’s spectrum was formed of exactly one ...

Weierstrass representation is a classical parameterization of minimal surfaces. However, two functions should be specified to construct the parametric form in Weierestrass representation. In this paper, we propose an explicit parametric form for a class of parametric polynomial minimal surfaces of arbitrary degree. It includes the classical Enneper surface for cubic case. The proposed minimal s...

We show that there exists a Martin-Löf random degree which has a strong minimal cover.

Given any graph $H$, a $G$ is said to be $q$-Ramsey for $H$ if every coloring of the edges with $q$ colors yields monochromatic subgraph isomorphic $H$. Such minimal additionally no proper $G'$ In 1976, Burr, Erdös, and Lovász initiated study parameter $s_q(H)$, defined as smallest minimum degree among all graphs this paper, we consider problem determining how many vertices $s_q(H)$ can contain...