Collapsible graphs and Hamiltonian connectedness of line graphs
نویسندگان
چکیده
منابع مشابه
Collapsible graphs and Hamiltonian connectedness of line graphs
Thomassen conjectured that every 4-connected line graph is Hamiltonian. Chen and Lai [Z.-H. Chen, H.-J. Lai, Reduction techniques for super-Eulerian graphs and related topics— an update, in: Ku Tung-Hsin (Ed.), Combinatorics and Graph Theory, vol. 95, World Scientific, Singapore/London, 1995, pp. 53–69, Conjecture 8.6] conjectured that every 3-edge connected, essentially 6-edge connected graph ...
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We investigate graphs G such that the line graph L(G) is hamiltonian connected if and only if L(G) is 3-connected, and prove that if each 3-edge-cut contains an edge lying in a short cycle of G, then L(G) has the above mentioned property. Our result extends Kriesell’s recent result in [J. of Combinatorial Theory, Ser. B. 82 (2001), 306-315] that every 4-connected line graph of a claw free graph...
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Thomassen conjectured that every 4-connected line graph is Hamiltonian. Chen and Lai (Combinatorics and Graph Theory, vol 95, World Scientific, Singapore, pp 53–69; Conjecture 8.6 of 1995) conjectured that every 3-edge connected and essentially 6-edge connected graph is collapsible. Denote D3(G) the set of vertices of degree 3 of graph G. For e = uv ∈ E(G), define d(e) = d(u)+ d(v)− 2 the edge ...
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A graph G is collapsible if for every even subset X ~ V(G), G has a subgraph r such that G E(J ') is connected and the set of odd-degree vertices of J' is X. A graph obtained by contracting all the non-trivial collapsible subgraphs of G is called the reduction of G. In this paper. we characterize graphs of diameter two in terms of collapsible subgraphs and investigate the relationship between t...
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Let A be a ®nite abelian group and G be a digraph. The boundary of a function f : E G 7! A is a function q f : V G 7! A given by q f v Pe leaving v f eÿ P e entering v f e. The graph G is A-connected if for every b : V G 7! A with P v AV G b v 0, there is a function f : E G 7! Aÿ f0g such that q f b. In [J. Combinatorial Theory, Ser. B 56 (1992) 165±182], Jaeger et al showed th...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2012
ISSN: 0166-218X
DOI: 10.1016/j.dam.2012.03.028