On graphs and algebraic graphs that do not contain cycles of length 4
نویسندگان
چکیده
We consider extremal problems for algebraic graphs, that is, graphs whose vertices correspond to vectors in Rd, where two vectors are connected by an edge according to an algebraic condition. We also derive a lower bound on the rank of the adjacency matrix of a general abstract graph using the number of 4-cycles and a parameter which measures how close the graph is to being regular. From this we derive a rank bound for the adjacency matrix A of any simple graph with n vertices and E edges which does not contain a copy of K2,r: rank(A) ≥ E−2n(r+1) r2√n .
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عنوان ژورنال:
- Journal of Graph Theory
دوره 68 شماره
صفحات -
تاریخ انتشار 2011