# Supereulerian graphs with small matching number and 2-connected hamiltonian claw-free graphs

@article{Xu2014SupereulerianGW, title={Supereulerian graphs with small matching number and 2-connected hamiltonian claw-free graphs}, author={Jinquan Xu and Ping Li and Zhengke Miao and Keke Wang and Hongyuan Lai}, journal={International Journal of Computer Mathematics}, year={2014}, volume={91}, pages={1662 - 1672} }

Motivated by the Chinese Postman Problem, Boesch, Suffel, and Tindell [The spanning subgraphs of Eulerian graphs, J. Graph Theory 1 (1977), pp. 79–84] proposed the supereulerian graph problem which seeks the characterization of graphs with a spanning Eulerian subgraph. Pulleyblank [A note on graphs spanned by Eulerian graphs, J. Graph Theory 3 (1979), pp. 309–310] showed that the supereulerian problem, even within planar graphs, is NP-complete. In this paper, we settle an open problem raised by…

## 9 Citations

### On the Independence Number of Traceable 2-Connected Claw-Free Graphs

- MathematicsDiscuss. Math. Graph Theory
- 2019

It is shown that every 2-connected claw-free graph with independence number α(G) ≤ 6 is traceable or belongs to two exceptional families of well-defined graphs.

### Supereulerian Graphs with Constraints on the Matching Number and Minimum Degree

- MathematicsGraphs Comb.
- 2021

Every connected simple graph G with δ (G) ≥ α ′ ( G) has a hamiltonian line graph.

### The Independence Number Conditions for 2-Factors of a Claw-Free Graph

- MathematicsAxioms
- 2022

In 2014, some scholars showed that every 2-connected claw-free graph G with independence number α(G)≤3 is Hamiltonian with one exception of family of graphs. If a nontrivial path contains only…

### On Supereulerian Digraphs

- Mathematics
- 2014

On Supereulerian Digraphs Mansour Jarbo Algefari A digraph D is eulerian if D is connected and for any v ∈ V (D), d+D(v) = d − D(v). A digraph D is supereulerian if D contains a spanning eulerian…

### Chvátal–Erdös Type Conditions for Hamiltonicity of Claw-Free Graphs

- MathematicsGraphs Comb.
- 2016

The main result implies that improvements to case (a) or (b) by increasing the value of r and by enlarging the collection of exceptional graphs can be obtained with the help of a computer.

### Supereulerian Digraphs with Large Arc‐Strong Connectivity

- MathematicsJ. Graph Theory
- 2016

It is proved that if, then D has a spanning eulerian subdigraph, and let be the arc-strong connectivity of D, and be the size of a maximum matching of D.

### A Condition on Hamilton-Connected Line Graphs

- MathematicsBulletin of the Malaysian Mathematical Sciences Society
- 2022

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