论文标题
使用图形的不可数的Hadwiger猜想和树木的特征
The Uncountable Hadwiger Conjecture and Characterizations of Trees Using Graphs
论文作者
论文摘要
我们证明，存在$λ$的非特殊树的存在等同于存在一个不可估量的彩色图，没有$ k_ {ω_1} $ size $λ$的少数，建立了特殊树号码与无可住的Hadwiger猜想之间的连接。还推导了使用图的Aronszajn，Kurepa和Suslin树的表征。引入了新的图形连接性概念，我们可以使用该图表表征弱紧凑的红衣主教。
We prove that the existence of a non-special tree of size $λ$ is equivalent to the existence of an uncountably chromatic graph with no $K_{ω_1}$ minor of size $λ$, establishing a connection between the special tree number and the uncountable Hadwiger conjecture. Also characterizations of Aronszajn, Kurepa and Suslin trees using graphs are deduced. A new generalized notion of connectedness for graphs is introduced using which we are able to characterize weakly compact cardinals.
