# Search results for: Hong‐Jian Lai

Journal of Graph Theory > 100 > 3 > 489 - 503

*supereulerian*if it has a spanning eulerian subgraph. Harary and Nash‐Williams in 1968 proved that the line graph of a graph $G$ is hamiltonian if and only if $G$ has a dominating eulerian subgraph, Jaeger in 1979 showed that every 4‐edge‐connected graph is supereulerian, and Catlin in 1988 proved that every graph with two edge‐disjoint spanning trees is a contractible configuration for supereulerianicity...

Journal of Graph Theory > 98 > 2 > 285 - 308

Graphs and Combinatorics > 2019 > 35 > 5 > 1001-1010

*V*is a set of vertices and

*E*is a set of non-empty subsets of

*V*called edges. If all edges of

*H*have the same cardinality

*r*, then

*H*is a

*r*-uniform hypergraph; if

*E*consists of all

*r*-subsets of

*V*, then

*H*is a complete

*r*-uniform hypergraph, denoted by $$K_n^r$$ K n r , where $$n=|V|$$ n = | V | . A hypergraph $$H'=(V',E')$$...

Journal of Combinatorial Optimization > 2019 > 38 > 3 > 887-910

*M*with a distinguished element $$e_0 \in E(M)$$ e 0 ∈ E ( M ) is a rooted matroid with $$e_0$$ e 0 being the root. We present a characterization of all connected binary rooted matroids whose root lies in at most three circuits, and a characterization of all connected binary rooted matroids whose root lies in all but at most three circuits. While there exist infinitely...

Graphs and Combinatorics > 2019 > 35 > 1 > 67-89

*G*is said to be

*pancyclic*if

*G*contains cycles of lengths from 3 to |

*V*(

*G*)|. For a positive integer

*i*, we use $$Z_i$$ Z i to denote the graph obtained by identifying an endpoint of the path $$P_{i+1}$$ P i + 1 with a vertex of a triangle. In this paper, we show that every 4-connected claw-free $$Z_8$$ Z 8 -free graph is either pancyclic or is the line graph of the Petersen...

Graphs and Combinatorics > 2018 > 34 > 6 > 1713-1721

Discrete Applied Mathematics > 2018 > 247 > C > 14-22

Journal of Graph Theory > 89 > 1 > 64 - 75

*D*is supereulerian if

*D*has a spanning closed ditrail. Bang‐Jensen and Thomassé conjectured that if the arc‐strong connectivity $\lambda \left(D\right)$ of a digraph

*D*is not less than the independence number $\alpha \left(D\right)$, then

*D*is supereulerian. A digraph is bipartite if its underlying graph is bipartite. Let ${\alpha}^{\prime}\left(D\right)$ be the size of a maximum matching of

*D*. We prove that if

*D*is a bipartite digraph satisfying $\lambda \left(D\right)\ge \lfloor $...

Journal of Graph Theory > 88 > 4 > 577 - 591

*D*of

*G*with ${d}_{D}^{+}\left(v\right)-{d}_{D}^{-}\left(v\right)=\beta \left(v\right)$ in ${Z}_{3}$ for every vertex $v\in V\left(G\right)$ is called a β‐orientation. A graph

*G*is ${Z}_{3}$‐connected if

*G*admits a β‐orientation for every zero‐sum function β. Jaeger et al. conjectured that every 5‐edge‐connected graph is ${Z}_{3}$‐connected. A graph is $\u27e8{Z}_{3}\u27e9$‐extendable at vertex

*v*if any preorientation at

*v*can be extended...

Discrete Mathematics > 2018 > 341 > 2 > 400-404

Discrete Mathematics > 2017 > 340 > 12 > 2995-3001

Discrete Applied Mathematics > 2017 > 222 > C > 166-171

Discrete Mathematics > 2017 > 340 > 5 > 1092-1097

Discrete Mathematics > 2017 > 340 > 2 > 243-251

Journal of Combinatorial Theory, Series B > 2017 > 122 > C > 167-186

Journal of Graph Theory > 84 > 2 > 191 - 201

*D*with $V\left(D\right)=\{{v}_{1},{v}_{2},...,{v}_{n}\}$ satisfies ${d}_{D}^{+}\left({v}_{i}\right)={d}_{i}^{+}$ and ${d}_{D}^{-}\left({v}_{i}\right)={d}_{i}^{-}$ for each

*i*with $1\le i\le n$, then

**d**is called a degree sequence of

*D*. If

*D*is a strict digraph, then

**d**is called a strict digraphic sequence. Let $\u27e8d\u27e9$ be the collection of digraphs with degree sequence

**d**. We characterize strict digraphic sequences

**d**...

Discrete Applied Mathematics > 2016 > 213 > C > 219-223

Journal of Graph Theory > 84 > 1 > 17 - 25

*D*be a simple digraph on $n>k$ vertices. We prove that If then

*D*must have a nontrivial subdigraph

*H*such that the strong arc connectivity of

*H*is at least $k+1$. We also show that this bound is best possible and present a constructive characterization for the extremal graphs.

Discrete Mathematics > 2016 > 339 > 10 > 2500-2510

Theoretical Computer Science > 2016 > 640 > C > 119-124