کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4656267 | 1343428 | 2008 | 13 صفحه PDF | دانلود رایگان |
We investigate how to modify a simple graph G combinatorially to obtain a sequentially Cohen–Macaulay graph. We focus on adding configurations of whiskers to G, where to add a whisker one adds a new vertex and an edge connecting this vertex to an existing vertex of G. We give various sufficient conditions and necessary conditions on a subset S of the vertices of G so that the graph G∪W(S), obtained from G by adding a whisker to each vertex in S, is a sequentially Cohen–Macaulay graph. For instance, we show that if S is a vertex cover of G, then G∪W(S) is a sequentially Cohen–Macaulay graph. On the other hand, we show that if G∖S is not sequentially Cohen–Macaulay, then G∪W(S) is not a sequentially Cohen–Macaulay graph. Our work is inspired by and generalizes a result of Villarreal on the use of whiskers to get Cohen–Macaulay graphs.
Journal: Journal of Combinatorial Theory, Series A - Volume 115, Issue 2, February 2008, Pages 304-316