Let $H \xrightarrow{s} G$ denote that any edge-coloring of $H$ by $s$ colors contains a monochromatic $G$. The degree Ramsey number $r_{\Delta}(G;s)$ is defined to be $\min \{ \Delta(H): H G \}$, and the bipartite $br_{\Delta}(G;s)$ \textrm{ } \chi(H) = 2 \}$. In this note, we show $r_{\Delta}(K_{m,n};s)$ linear on $n$ with fixed $m$. We also evaluate for paths other trees.

In this survey, we discuss computability spectra of countable structures that provide a natural measure non-computability structure. This notion is main tool for investigating algorithmic properties structures. Along with review known results in field, present proofs some new to illustrate the method interpretation, which basic field. We also open questions.