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JCT
2006
93views more  JCT 2006»
14 years 9 months ago
On the minimal degree implying equality of the largest triangle-free and bipartite subgraphs
Erdos posed the problem of finding conditions on a graph G that imply t(G) = b(G), where t(G) is the largest number of edges in a triangle-free subgraph and b(G) is the largest nu...
József Balogh, Peter Keevash, Benny Sudakov
DM
2008
83views more  DM 2008»
14 years 10 months ago
The polynomial degrees of Grassmann and Segre varieties over GF(2)
A recent proof that the Grassmannian G1;n;2 of lines of PG(n; 2) has polynomial degree n 2 1 is outlined, and is shown to yield a theorem about certain kinds of subgraphs of any (...
R. Shaw
JGT
2008
77views more  JGT 2008»
14 years 9 months ago
Graph classes characterized both by forbidden subgraphs and degree sequences
: Given a set F of graphs, a graph G is F-free if G does not contain any member of F as an induced subgraph. We say that F is a degree-sequence-forcing set if, for each graph G in ...
Michael D. Barrus, Mohit Kumbhat, Stephen G. Hartk...
DM
2010
89views more  DM 2010»
14 years 10 months ago
Large induced subgraphs with equated maximum degree
For a graph G, denote by fk(G) the smallest number of vertices that must be deleted from G so that the remaining induced subgraph has its maximum degree shared by at least k verti...
Yair Caro, Raphael Yuster
WG
2005
Springer
15 years 3 months ago
Induced Subgraphs of Bounded Degree and Bounded Treewidth
We prove that for all 0 ≤ t ≤ k and d ≥ 2k, every graph G with treewidth at most k has a ‘large’ induced subgraph H, where H has treewidth at most t and every vertex in ...
Prosenjit Bose, Vida Dujmovic, David R. Wood