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JCT
2006
93views more  JCT 2006»
13 years 5 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»
13 years 5 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»
13 years 5 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»
13 years 5 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
13 years 10 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