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

Nash-Williams and Tutte independently characterized when a graph has k edgedisjoint spanning trees; a consequence is that 2k-edge-connected graphs have k edgedisjoint 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 than… (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)

- 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) ≤ hc(G) ≤ γc(G) ≤ h(G) + 1, where h(G), hc(G), and γc(G), respectively, are the minimum sizes of a hub set in G, a hub set inducing a connected subgraph, and a connected dominating set. Furthermore, all… (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 graphtheoretic 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)

- 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 χl(G) = χ(G).

- Jonathan A. Noel, Douglas B. West, Hehui Wu, Xuding Zhu
- Eur. J. Comb.
- 2015

Let ch(G) denote the choice number of a graph G (also called “list chromatic number” or “choosability” of G). Noel, Reed, and Wu proved the conjecture of Ohba that ch(G) = χ(G) when |V (G)| ≤ 2χ(G) + 1. We extend this to a general upper bound: ch(G) ≤ max{χ(G), ⌈(|V (G)| + χ(G)− 1)/3⌉}. Our result is sharp for |V (G)| ≤ 3χ(G) using Ohba’s examples, and it… (More)

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

The Chvátal–Erdős 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.

- Ross Churchley, Bojan Mohar, Hehui Wu
- SODA
- 2016

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

It is shown that every (2p+ 1) log2(|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), |∂G(U)| ≥ (2p+ 1)||U ∩ V | − |U ∩ V −||. These extend former results by Da Silva and Dahad on nowhere zero 3-flows of 5-regular… (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 Ryjác̆ek’s line graph closure, it follows that every 3-connected, essentially 11-connected claw-free graph is… (More)