论文标题
对默克的猜想在3个连接的立方平面图上具有较大循环频谱间隙
Counterexamples to a conjecture of Merker on 3-connected cubic planar graphs with a large cycle spectrum gap
论文作者
论文摘要
默克（Merker）猜想，如果$ k \ ge 2 $是整数，而$ g $ a 3连接的立方体平面图至少$ k $，则$ g $的周期长度的集合必须至少包含间隔$ [k，2k，2k+2] $的至少一个元素。我们在这里证明，对于每一个均匀的整数$ k \ ge 6 $，都有一个无限的反例。
Merker conjectured that if $k \ge 2$ is an integer and $G$ a 3-connected cubic planar graph of circumference at least $k$, then the set of cycle lengths of $G$ must contain at least one element of the interval $[k, 2k+2]$. We here prove that for every even integer $k \ge 6$ there is an infinite family of counterexamples.
