Oddness to resistance ratios in cubic graphs

  title={Oddness to resistance ratios in cubic graphs},
  author={Imran Allie},
  journal={Discrete Mathematics},
Abstract Let G be a bridgeless cubic graph. Oddness (weak oddness) is defined as the minimum number of odd components in a 2-factor (an even factor) of G , denoted as ω ( G ) (Steffen, 2004) ( ω ′ ( G ) Lukot’ka and Mazak (2016)). Oddness and weak oddness have been referred to as measurements of uncolourability (Fiol et al., 2017, Lukot’ka and Mazak, 2016, Lukot’ka et al., 2015 and, Steffen, 2004), due to the fact that ω ( G ) = 0 and ω ′ ( G ) = 0 if and only if G is 3-edge-colourable. Another… CONTINUE READING

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