Spanning subgraph with Eulerian components
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TL;DR: It is proved that if G is a connected graph with F(G)@?k, then either G is k-supereulerian or G can be contracted to a tree of order k+1.
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About: This article is published in Discrete Mathematics. The article was published on 01 Mar 2012. and is currently open access. The article focuses on the topics: Graph factorization & Spanning tree.
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Citations
Supereulerianity of k-edge-connected graphs with a restriction on small bonds
Zhaohong Niu,Liming Xiong +1 more
TL;DR: It is shown that if [email protected]?C"3(10,m) with n>11m, then either G is supereulerian or it is contractible to the Petersen graph.
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Even factor of a graph with a bounded number of components
Zhaohong Niu,Liming Xiong +1 more
- 01 Jan 2010
TL;DR: This paper proves that if δ(G) ≥� n/k �− 1, then the (collapsible) reduction Gof G satisfies |V (G � ) |≤ k, and the preimage of each vertex of G is nontrivial, and it is shown that every 2-edge- connected reduced graph of order n ≤ 3k +1 ≤ 10 has a spanning even subgraph with at most k components.
Catlin’s reduced graphs with small orders
TL;DR: A graph is considered to be supereulerian if it has a spanning closed trail as mentioned in this paper, and the problem of determining the reduced nonsupereulerians with small orders is NP-hard.
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On extremal k-supereulerian graphs
TL;DR: Niu and Xiong as discussed by the authors showed that any 2-edge-connected simple graph G with n > 5 k + 2 vertices is k-supereulerian.
1
Smallest k-edge-connected claw-free graphs without special spanning trails
Zhaohong Niu,Liming Xiong +1 more
- 01 Jan 2014
TL;DR: In this article, the smallest 2-edge-connected non-traceable graph G1, G2 without a spanning trail and the smallest k-edge connected non-supereulerian claw-free graph for k = 2, 3.
References
•Book
Graph theory with applications
J. A. Bondy
- 01 Jan 1976
TL;DR: In this paper, the authors present Graph Theory with Applications: Graph theory with applications, a collection of applications of graph theory in the field of Operational Research and Management. Journal of the Operational research Society: Vol. 28, Volume 28, issue 1, pp. 237-238.
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A reduction method to find spanning Eulerian subgraphs
TL;DR: A general method to find a spanning eulerian subgraph of G such that the vertices of odd degree in Γ form a specified set S ⊆ V(G), such that G - E(Γ) is connected.
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