Question

Show that for all integers $k \ge 2$ every graph $G$ contains a $k$-partite subgraph $H$ with $e(H) \ge \frac{k-1}{k}e(G)$.

score 576 · Answer 1 · 2017-10-28 11:32:00

576

Views

Show that for all integers $k \ge 2$ every graph $G$ contains a $k$-partite subgraph $H$ with $e(H) \ge \frac{k-1}{k}e(G)$.

Published on 28 Oct 2017 - 11:32

score 419 · Answer 2 · 2017-10-29 13:41:17

Use Hall's Theorem to show if $|N(S)|\geq k|S|$ for all $\emptyset \neq S \subseteq A$, vertices of $G$ can be covered entirely by disjoint $k$-stars.

score 1.2k · Answer 3 · 2017-10-29 20:10:34

1.2k

Views

Bipartite Graphs and Perfect Matchings when |A|=|B|=n

Published on 29 Oct 2017 - 20:10

score 182 · Answer 4 · 2026-03-26 17:46:42

182

Views

on theorem 5.3 in bondy and murty's book on matching and coverings

Published on 26 Mar 2026 - 17:46

score 1.1k · Answer 5 · 2026-03-26 19:18:56

1.1k

Views

Application of Hall's theorem to find a matching of a specific size

Published on 26 Mar 2026 - 19:18

score 501 · Answer 6 · 2026-03-26 19:15:48

501

Views

Construct a bipartite graph satisfying a condition

Published on 26 Mar 2026 - 19:15

score 133 · Answer 7 · 2026-03-26 13:02:15

133

Views

existence of $(K,\alpha)$-disperser with degree $D=O(\log\frac{N}{K})$

Published on 26 Mar 2026 - 13:02

score 2.1k · Answer 8 · 2026-03-26 03:00:17

2.1k

Views

Largest eigenvalue of a normalized graph Laplacian

Published on 26 Mar 2026 - 3:00

score 723 · Answer 9 · 2017-11-10 08:14:43

723

Views

Proving Coloring for odd-length Circuits

Published on 10 Nov 2017 - 8:14

score 36 · Answer 10 · 2017-11-12 01:39:55

Can the owner assign one worker from each station to be the manager of that station in such a way that a worker is the manager of at most one station?