Whiskers and sequentially Cohen-Macaulay graphs

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dc.creatorFrancisco, Christopher A.
dc.creatorHa, Huy Tai
dc.date2006-05-17
dc.date2008-06-06
dc.date.accessioned2026-07-07T09:42:53Z
dc.date.available2026-07-07T09:42:53Z
dc.descriptionLet G be a simple (i.e., no loops and no multiple edges) graph. We investigate the question of how to modify G combinatorially to obtain a sequentially Cohen-Macaulay graph. We focus on modifications given by 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 in G. We give various sufficient conditions and necessary conditions on a subset S of the vertices of G so that the graph G \cup 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 \cup W(S) is a sequentially Cohen-Macaulay graph. On the other hand, we show that if G \backslash S is not sequentially Cohen-Macaulay, then G \cup 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.
dc.descriptionfinal version: contains minor revisions, improved exposition
dc.identifierhttps://arxiv.org/abs/math/0605487
dc.identifierhttp://arxiv.org/abs/math/0605487
dc.identifierJ. Combin. Theory Ser. A 115 (2008), no. 2, 304-316
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/162349
dc.subjectCommutative Algebra
dc.subjectCombinatorics
dc.subject13C14, 13D02, 05C38, 05C75
dc.titleWhiskers and sequentially Cohen-Macaulay graphs
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