论文标题
图形和超图的总版本的1-2-3键入
On the total versions of 1-2-3-conjecture for graphs and hypergraphs
论文作者
论文摘要
2004年，Karoński，oluczak和Thomason提出了$ 1 $ - $ 2 $ - $ 3 $ - 注射：对于每个漂亮的图形$ g $，都有一个边缘加权函数$ W： 之后，文献中提出了这种猜想的总版本，最近，Kalkowski等人。已将这种猜想推广到超图。在本文中，有关总版本的一些先前已知的结果得到了改善。此外，对于一些著名的超图系列，例如完整的$ n $ - 局部超图，路径，循环，Theta HyperGraphs和一些几何平面，给出了肯定的答案。同样，基于相应的参数对这些超图进行表征。
In 2004, Karoński, Łuczak and Thomason proposed $1$-$2$-$3$-conjecture: For every nice graph $G$ there is an edge weighting function $ w:E(G)\rightarrow\{1,2,3\} $ such that the induced vertex coloring is proper. After that, the total versions of this conjecture were suggested in the literature and recently, Kalkowski et al. have generalized this conjecture to hypergraphs. In this paper, some previously known results on the total versions are improved. Moreover, an affirmative answer is given to the conjecture for some well-known families of hypergraphs like complete $n$-partite hypergraphs, paths, cycles, theta hypergraphs and some geometric planes. Also, these hypergraphs are characterized based on the corresponding parameter.
