**Definition.** Suppose $H=(V,E)$ is a hypergraph. Call a hyperedge $e=\{v_1,v_2,\dotsc,v_k\}$ a **$k$-star** if in the 1-skeleton of $H$ there is a copy of $K^{1,k-1}$ whose union equals $e$. (Obviously in the case  $k=2$, $e$ is an usual edge.)

**EDITED:** Consider the following two properties:

  (a) For every hyperedge $e$ of $H$ there exists $k\in\mathbb{N}$ such that $e$ is $k$-star.

 (b) If two hyperedges $e_i$ and $e_j$ which share at least one vertices ($|e_i\cap e_j|\geq1$) then there is an usual edge that connect internal nodes of this two hyperedges.


>**Question:** Does anybody know how to prove or disprove the following guess about edge coloring of Hypergraphs?

Let $\Delta(H)$ denote the maximum of vertex-degrees of a finite hypergraph $H$. 

>>**Guess.** Let $H$ be a simple hypergraph satisfying (a) and (c). Then there exists an $(\Delta+1)$-edge-coloring so that any two edges which share one vertices have distinct colors.