منابع مشابه
On Turáns theorem for sparse graphs
a?nl(t+1) where a denotes the maximum size of an independent set in G. We improve this bound for graphs containing no large cliques. 0. Notation n=n(G)=number of vertices of the graph G e=e(G)=number of edges of G h=h(G)=number of triangles in G deg (P)=valency (degree) of the vertex P deg, (P) = triangle-valency of P=number of triangles in G adjacent to P t=t(G)=n f deg (P) = 2eln = average va...
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We are motivated by the analogue of Turán’s theorem in the hypercube Qn: how many edges can a Qd-free subgraph of Qn have. We study this question through its Ramsey-type variant and obtain asymptotic results. We show that for every odd d it is possible to color the edges of Qn with (d+1)2 4 colors, such that each subcube Qd is polychromatic, that is, contains an edge of each color. The number o...
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The hypercube Qn is the graph whose vertex set is {0, 1}n and where two vertices are adjacent if they differ in exactly one coordinate. For any subgraph H of the cube, let ex(Qn,H) be the maximum number of edges in a subgraph of Qn which does not contain a copy of H. We find a wide class of subgraphs H, including all previously known examples, for which ex(Qn,H) = o(e(Qn)). In particular, our m...
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Let Qn be a hypercube of dimension n, that is, a graph whose vertices are binary n-tuples and two vertices are adjacent iff the corresponding n-tuples differ in exactly one position. An edge coloring of a graph H is called rainbow if no two edges of H have the same color. Let f(G, H) be the largest number of colors such that there exists an edge coloring of G with f(G, H) colors such that no su...
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Body centered structures are used as seeds for a variety of structures of rank 3 and higher. Propellane based structures are introduced and their design and topological properties are detailed.
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2007
ISSN: 0895-4801,1095-7146
DOI: 10.1137/060649422