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A (k; g)-graph is a k-regular graph with girth g. A (k; g)-cage is a (k; g)-graph with the least number of vertices. In this note, we show that (k; g)-cage has an r-factor of girt...

Guizhen Liu, Qinglin Yu

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93

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ARSCOM
2008

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Total Perfect Codes in Tensor Products of Graphs

14 years 10 months ago

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A total perfect code in a graph is a subset of the graph's vertices with the property that each vertex in the graph is adjacent to exactly one vertex in the subset. We prove t...

Ghidewon Abay-Asmerom, Richard Hammack, Dewey T. T...

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78

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ARSCOM
2008

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Estimating the number of graphs containing very long induced paths

14 years 12 months ago

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Let P(n, k) denote the number of graphs on n + k vertices that contain Pn, a path on n vertices, as an induced subgraph. In this note we will find upper and lower bounds for P(n, ...

Steven Butler

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