论文标题
最大无连锁图的新界限
New bounds on maximal linkless graphs
论文作者
论文摘要
我们在$ n $顶点上建立了一个最大无连锁的可嵌入图，所有$ n \ ge 10 $的$ 3n-5 $边缘，另一个在$ n $ dertices上和$ m <\ frac {25n} {12n} {12} {12} {12} - \ frac {1} {1} {1} {4} {4} {4} {4} {4} $ n \ ge for $ n \ ge 13 $ 13 $ 13 $ 13 $ 13 $。后者显着提高了任何以前已知的无限家族的边缘与vertex的比率最低。我们构建了一个图形系列，表明一类最大链接的可嵌入图与最大的图形不同，而图形最大，而没有L. Jorgensen研究的$ k_6 $ binor。我们提供了必要的条件，即当两个最大可连接的可嵌入图的集团总和超过$ k_2 $，$ k_3 $或$ k_4 $是一个最大的无连锁图形图，并使用这些结果来证明我们的构造产生最大的链接无链接图形。
We construct a family of maximal linklessly embeddable graphs on $n$ vertices and $3n-5$ edges for all $n\ge 10$, and another family on $n$ vertices and $m< \frac{25n}{12}-\frac{1}{4}$ edges for all $n\ge 13$. The latter significantly improves the lowest edge-to-vertex ratio for any previously known infinite family. We construct a family of graphs showing that the class of maximal linklessly embeddable graphs differs from the class of graphs that are maximal without a $K_6$ minor studied by L. Jorgensen. We give necessary and sufficient conditions for when the clique sum of two maximal linklessly embeddable graphs over $K_2$, $K_3$, or $K_4$ is a maximal linklessly embeddable graph, and use these results to prove our constructions yield maximal linklessly embeddable graphs.
