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A Characterization of Non-Hamiltonian Graphs With Large Degrees
Annals of Discrete Mathematics 9 (1980) 259 @ North-Holland Publishing Company.
A CHARACTERIZATION OF NON-HAMILTONIAN GRAPHS
WITH LARGE DEGREES Roland HAGGKVIST
University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada
Abstract Using standard notation we put S(G) = minimum vertex-degree in G, v(G) = cardinality of the vertex-set in G, ar(G)=cardinality of a maximum stable set in G (i.e. the maximum number of pairwise non-adjacent vertices in G).
Sample Theorems. (1) Let G be a non-hamiltonian 2-connected graph with S>$(v+2). Then G contains a stable set of four vertices with at most a ( G ) - l neighbours altogether. (2) Let G be a non-hamiltonian 2-connected graph with S a i ( v + 2 ) . Then G contains a stable set of [i(v+lo)] vertices with at most $(v- 1) neighbours altogether. (3) Let G be a non-hamiltonian 2-connected graph with tSa&v. Then G contains a set of rn 3 z v vertices whose deletion leaves a graph which cannot be (vertex-) covered by rn paths.
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A CHARACTERIZATION OF NON-HAMILTONIAN GRAPHS
WITH LARGE DEGREES Roland HAGGKVIST
University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada
Abstract Using standard notation we put S(G) = minimum vertex-degree in G, v(G) = cardinality of the vertex-set in G, ar(G)=cardinality of a maximum stable set in G (i.e. the maximum number of pairwise non-adjacent vertices in G).
Sample Theorems. (1) Let G be a non-hamiltonian 2-connected graph with S>$(v+2). Then G contains a stable set of four vertices with at most a ( G ) - l neighbours altogether. (2) Let G be a non-hamiltonian 2-connected graph with S a i ( v + 2 ) . Then G contains a stable set of [i(v+lo)] vertices with at most $(v- 1) neighbours altogether. (3) Let G be a non-hamiltonian 2-connected graph with tSa&v. Then G contains a set of rn 3 z v vertices whose deletion leaves a graph which cannot be (vertex-) covered by rn paths.
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