**Definition.** Call an hyperedge $e=\{v_1,v_2,...,v_k\}$, **$k$-star**
 ($k\geq 3$) if all its vertices form a $k$-star graph. i.e. a tree with one internal node and $k-1$ leaves. Obviously in the case  $k=2$, $e$ is an usual edge.

**EDITED:** Consider the following three properties:

 (a) All hyperedges of $H$ are of the form $k$-star for some $k\in \Bbb N$;

 (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.

 (c) between any two hyperedges $e_i$ and $e_j$ we have

$$\text{internal node $\not\in e_i\cap e_j$} $$

>**Question:** Does anybody know how to prove or disprove the following guess about edge coloring of Hypergraphs?
>>**Guess.** Let $H$ be a simple hypergraph satisfies in (a), (b) and (c). Then there exists an $(\Delta +1)$-
edge-coloring so that any two edges which share one vertices have distinct colors where each vertex is of degree at most $\Delta$.