#### Filter Results:

- Full text PDF available (21)

#### Publication Year

2005

2017

- This year (1)
- Last 5 years (12)
- Last 10 years (21)

#### Publication Type

#### Co-author

#### Publication Venue

#### Key Phrases

Learn More

- Douglas B. West, Hehui Wu
- J. Comb. Theory, Ser. B
- 2012

Nash-Williams and Tutte independently characterized when a graph has k edge-disjoint spanning trees; a consequence is that 2k-edge-connected graphs have k edge-disjoint spanning trees. Kriesell conjectured a more general statement: defining a set S ⊆ V (G) to be j-edge-connected in G if S lies in a single component of any graph obtained by deleting fewer… (More)

- Hong-Jian Lai, Yehong Shao, Hehui Wu, Ju Zhou
- J. Comb. Theory, Ser. B
- 2009

It is shown that every (2p + 1) log 2 (|V (G)|)-edge-connected graph G has a mod (2p + 1)-orientation, and that a (4p + 1)-regular graph G has a mod (2p + 1)-orientation if and only if V (G) has a partition (V + , V −) such that ∀U ⊆ V (G), These extend former results by Da Silva and Dahad on nowhere zero 3-flows of 5-regular graphs, and by Lai and Zhang on… (More)

- Suil O, Douglas B. West, Hehui Wu
- 2010

The Chvátal–Erd˝ os Theorem states that every graph whose connectivity is at least its independence number has a spanning cycle. In 1976, Fouquet and Jolivet conjectured an extension: If G is an n-vertex k-connected graph with independence number a, and a ≥ k, then G has a cycle with length at least k(n+a−k) a. We prove this conjecture.

- Tracy Grauman, Stephen G. Hartke, +5 authors Hehui Wu
- Inf. Process. Lett.
- 2008

A hub set in a graph G is a set U ⊆ V (G) such that any two vertices outside U are connected by a path whose internal vertices lie in U. We prove that h(G) ≤ h c (G) ≤ γ c (G) ≤ h(G) + 1, where h(G), h c (G), and γ c (G), respectively, are the minimum sizes of a hub set in G, a hub set inducing a connected subgraph, and a connected dominating set.… (More)

- Yogesh Anbalagan, Hao Huang, Shachar Lovett, Sergey Norin, Adrian Vetta, Hehui Wu
- APPROX-RANDOM
- 2015

We prove that for any constant k and any < 1, there exist bimatrix win-lose games for which every-WSNE requires supports of cardinality greater than k. To do this, we provide a graph-theoretic characterization of win-lose games that possess-WSNE with constant cardinality supports. We then apply a result in additive number theory of Haight [8] to construct… (More)

- Hong-Jian Lai, Yehong Shao, Hehui Wu, Ju Zhou
- J. Comb. Theory, Ser. B
- 2006

Thomassen conjectured that every 4-connected line graph is Hamiltonian. A vertex cut X of G is essential if G − X has at least two non-trivial components. We prove that every 3-connected, essentially 11-connected line graph is Hamiltonian. Using Ryjá˘ cek's line graph closure, it follows that every 3-connected, essentially 11-connected claw-free graph is… (More)

A parity walk in an edge-coloring of a graph is a walk traversing each color an even number of times. We introduce two parameters. Let p(G) be the least number of colors in a parity edge-coloring of G (a coloring having no parity path). Let b p(G) be the least number of colors in a strong parity edge-coloring of G (a coloring having no open parity walk).… (More)

- Jonathan A. Noel, Bruce A. Reed, Hehui Wu
- Journal of Graph Theory
- 2015

We prove a conjecture of Ohba which says that every graph G on at most 2χ(G) + 1 vertices satisfies χ ℓ (G) = χ(G).

- József Balogh, John Lenz, Hehui Wu
- Discussiones Mathematicae Graph Theory
- 2011

The Hadwiger number h(G) of a graph G is the maximum size of a complete minor of G. Hadwiger's Conjecture states that h(G) ≥ χ(G). Since χ(G)α(G) ≥ |V (G)|, Hadwiger's Conjecture implies that α(G)h(G) ≥ |V (G)|. We show that (2α(G) − ⌈log τ (τ α(G)/2)⌉)h(G) ≥ |V (G)| where τ ≈ 6.83. For graphs with α(G) ≥ 14, this improves on a recent result of… (More)

- Hong-Jian Lai, Yehong Shao, Ju Zhou, Hehui Wu
- 2005

A graph is claw-free if it does not have an induced subgraph isomorphic to a K 1,3. In this paper, we proved the every 3-connected, essentially 11-connected claw-free graph is hamiltonian. We also present two related results concerning hamiltonian claw-free graphs.