Sum choice number of generalized θ-graphs

Sum-list-colouring of θ-hypergraphs

“…The question is, whether we should expect that an sc-greedy graph be obtained by adding a G-path to an sc-greedy θ-graph. In [3] the authors proved that χ sc (G) + 2s ≤ χ sc (G 1 ) ≤ χ sc (G) + 2s + 1 if G 1 is the result of adding a G-path on s + 2 vertices to an arbitrary simple graph G, assuming that s ≥ 1. They did not consider the case when a G-path has 2 vertices, which seems to be very important.…”

“…In [9] the upper bound on the minimum sum of the list sizes was determined. Graphs that meet this bound, known as sc-greedy, led themselves to a very popular line of investigation in the literature ( [2], [3], [7], [9], [12]). In [5], the authors analyzed sum-list-colouring concept assuming that colour classes need not be edgeless.…”

Sum-list colouring of unions of a hypercycle and a path with at most two vertices in common

“…Thus, in every L-colouring of H such that vertices of P 1 ∪ P 2 ∪ P 3 are properly coloured, the vertices in 3 1 are coloured with a or the vertices in…”

“…, v 3 1 = w, putting in each step the colour from the list that guarantees φ to be proper on P 3 . Finally, we assign to w the colour from its list that is different from φ(v 1 ), φ(v 2 ) and φ(v 3 2 ).…”

“…Among others Heinold [8] investigated the sum-list colourability of θ-graphs. Brause et al [3] determined upper bounds on the sum-choice-numbers of all generalized θ-graphs θ k 1 k 2 •••kr , where k i ≥ 2 for every i, and next they characterized all generalized θ-graphs G that attain the upper bound |V (G)| + |E(G)|. Graphs that meet this bound, named sc-greedy, gain a lot of attention in the literature.…”