
A Note on Colourings of Connected 2edge Coloured Cubic Graphs
In this short note we show that every connected 2edge coloured cubic gr...
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A Note on Colourings of Connected Oriented Cubic Graphs
In this short note we show that every connected oriented cubic graph adm...
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Embedding quadratization gadgets on Chimera and Pegasus graphs
We group all known quadratizations of cubic and quartic terms in binary ...
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Normal edgecolorings of cubic graphs
A normal kedgecoloring of a cubic graph is an edgecoloring with k col...
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The Component Diagnosability of General Networks
The processor failures in a multiprocessor system have a negative impact...
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Meyniel's conjecture on graphs of bounded degree
The game of Cops and Robbers is a well known pursuitevasion game played...
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Minimum status, matching and domination of graphs
The minimum status of a graph is the minimum of statuses of all vertices...
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On the minimum leaf number of cubic graphs
The minimum leaf number ml (G) of a connected graph G is defined as the minimum number of leaves of the spanning trees of G. We present new results concerning the minimum leaf number of cubic graphs: we show that if G is a connected cubic graph of order n, then ml(G) ≤n/6 + 1/3, improving on the best known result in [Inf. Process. Lett. 105 (2008) 164169] and proving the conjecture in [Electron. J. Graph Theory and Applications 5 (2017) 207211]. We further prove that if G is also 2connected, then ml(G) ≤n/6.53, improving on the best known bound in [Math. Program., Ser. A 144 (2014) 227245]. We also present new conjectures concerning the minimum leaf number of several types of cubic graphs and examples showing that the bounds of the conjectures are best possible.
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