解离数的一个界
A bound on the dissociation number
摘要：
图$G$的解离数${\rm diss}(G)$是指图$G$的顶点集的最大阶数，该顶点集导出的子图的最大度至多为$1$ .计算给定图的解离数在算法上是困难的，即使是在限制为次立方二部图的情况下。对于图$G$与$n$顶点，$m$边，$k$组件，和$c_1$诱导周期的长度$1$模$3$，我们显示${\rm diss}(G)\geq n-\frac{1}{3}\Big(m+k+c_1\Big)$。此外，我们还刻画了每两个圈都是点不相交的极图。
英文摘要：
The dissociation number ${\rm diss}(G)$ of a graph $G$ is the maximum order of a set of vertices of $G$ inducing a subgraph that is of maximum degree at most $1$. Computing the dissociation number of a given graph is algorithmically hard even when restricted to subcubic bipartite graphs. For a graph $G$ with $n$ vertices, $m$ edges, $k$ components, and $c_1$ induced cycles of length $1$ modulo $3$, we show ${\rm diss}(G)\geq n-\frac{1}{3}\Big(m+k+c_1\Big)$. Furthermore, we characterize the extremal graphs in which every two cycles are vertex-disjoint.
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