3 problems

The Bollobás–Nikiforov conjecture for $K_4$ -free graphs
Let $G$ be a $K_4$ -free graph with $m$ edges, and let … be the adjacency eigenvalues of $G$ . Bollobás–Nikiforov conjecture for $K_4$ -free graphs. If $G\neq K_3$ , then … This is the…
openextremal-graph-theory k4-free-graphs spectral-graph-theory
0 responses
05
Győri–Keszegh's greedy-partition triangle conjecture for $K_4$ -free graphs
Győri–Keszegh's conjecture. For every such graph $G$ and every greedy partition $P$ ,
openextremal-graph-theory k4-free-graphs triangle-packings
0 responses
010
Chung–Graham conjecture for sparse halves in $K_4$ -free graphs
Let $G$ be a $K_4$ -free graph on $n$ vertices. Chung–Graham conjecture. $G$ contains a vertex set of size … that spans at most $n^2/18$ edges. The bound is best possible, as shown…
openextremal-graph-theory k4-free-graphs
0 responses
06

The Bollobás–Nikiforov conjecture for K4K_4K4​-free graphs