论文标题
图形可实现的整数序列的一些标准
Some criteria for integer sequences pair being realizable by a graph
论文作者
论文摘要
令$ a =（a_1，\ ldots，a_n）$和$ b =（b_1，\ ldots，b_n）$是两个非负整数的序列，带有$ a_i \ le b_i $ for $ a_i \ le b_i $ for $ 1 \ le i \ le i \ le i \ le n $。如果存在一个简单的图形$ g $，则可以通过图实现对$（a; b）$，v_1，\ ldots，v_n $，因此$ a_i \ le d_g（v_i）\ le b_i $ for $ a_i \ le b_i $ for $ 1 \ le le i \ le i \ le i \ le i \ le i \ le i \ le n $。令$ \ prepeq $表示词典订购$ z \ times z：$ $（a_ {i+1}，b_ {i+1}）\ preceq（a_i，b_i）\ longleftrightArrow [（a_ {a_ {i+1} （（（a_ {i+1} = a_i）\＆（b_ {i+1} \ le b_i））$。我们说，如果$（a_ {i+1}，b_ {i+1}）\ prepeq（a_i，b_i）$，序列$ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a。在本文中，我们考虑了由于Berge，Ryser等人的序列对六个经典表征的概括。并提供相关的结果。
Let $A=(a_1,\ldots,a_n)$ and $B=(b_1,\ldots,b_n)$ be two sequences of nonnegative integers with $a_i \le b_i$ for $1\le i\le n$. The pair $(A;B)$ is said to be realizable by a graph if there exists a simple graph $G$ with vertices $v_1,\ldots, v_n$ such that $a_i\le d_G(v_i)\le b_i$ for $1\le i\le n$. Let $\preceq$ denote the lexicographic ordering on $Z\times Z:$ $(a_{i+1},b_{i+1})\preceq (a_i,b_i)\Longleftrightarrow [(a_{i+1}<a_i)\vee ((a_{i+1}=a_i)\&(b_{i+1}\le b_i))]$. We say that the sequences $A$ and $B$ are in good order if $(a_{i+1},b_{i+1})\preceq (a_i,b_i)$. In this paper, we consider the generalizations of six classical characterizations on sequences pair due to Berge, Ryser et al. and present related results.
