Zhang et al.'s conjecture on adjacent vertex distinguishing total colourings

Let GG be a graph, and let χat(G)\chi_{at}(G) denote its adjacent vertex distinguishing total chromatic number, the least number of colours in a proper total colouring such that every pair of adjacent vertices has a different set of colours appearing on the vertex and its incident edges. Zhang et al.'s conjecture. For every graph GG,

χat(G)Δ(G)+3.\chi_{at}(G)\leq \Delta(G)+3.

The conjecture seeks a sharp general upper bound for adjacent vertex distinguishing total colourings. The source gives no resolution, so the conjecture remains open.

Sources & referencesView supporting material

Primary source

Tom Coker and Karen Johannson, “The adjacent vertex distinguishing total chromatic number”, arXiv:1009.1785 (2010).

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