منابع مشابه
Bounding the bandwidths for graphs
Let G;H be nite graphs with |V (H)|¿|V (G)|. The bandwidth of G with respect to H is de ned to be BH (G) = min maxuv∈E(G) dH ( (u); (v)), with the minimum taken over all injections from V (G) to V (H), where dH (x; y) is the distance in H between two vertices x; y ∈ V (H). This number is involved with the VLSI design and optimization, especially when the “host” graph H is a path Pn or a cycle C...
متن کاملBounding cochordal cover number of graphs via vertex stretching
It is shown that when a special vertex stretching is applied to a graph, the cochordal cover number of the graph increases exactly by one, as it happens to its induced matching number and (Castelnuovo-Mumford) regularity. As a consequence, it is shown that the induced matching number and cochordal cover number of a special vertex stretching of a graph G are equal provided G is well-covered bipa...
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We investigate the number of plane geometric, i.e., straight-line, graphs, a set S of n points in the plane admits. We show that the number of plane graphs is minimized when S is in convex position, and that the same result holds for several relevant subfamilies. In addition we construct a new extremal configuration, the so-called double zig-zag chain. Most noteworthy this example bears Θ∗( √ 7...
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A function f bounds graphs from above if there exists an infinite family of graph G, such that if G ∈ G then f(|VG|) = |EG| and for all nonempty subgraphs H of G we have that F (|VH |) ≥ |EH |. This paper considers the question: which functions bound graphs? keywords graphs, extremal graph theory AMS subject classification 05C99
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Given two graphs H1 and H2, a graph G is (H1,H2)-free if it contains no subgraph isomorphic to H1 or H2. Let Pt and Cs be the path on t vertices and the cycle on s vertices, respectively. In this paper we show that for any (P6, C4)-free graph G it holds that χ(G) ≤ 3 2 ω(G), where χ(G) and ω(G) are the chromatic number and clique number of G, respectively. Our bound is attained by several graph...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2000
ISSN: 0304-3975
DOI: 10.1016/s0304-3975(00)00068-2