… To support further our conjecture on the minimum possible product of the HajÃos number
of a graph and its complement, we find the minimum possible HajÃos number …

… The procedure for adding an edge is essentially the same, except that we use the graphs
Kq[1] or Kq + e depending on whether the extra edge has a vertex in the copy of Kq or not. …

… We relate Hajós’ conjecture to Ramsey theory, perfect graphs, and the … On the other hand,
we show that some of the graphs which Catlin conjectured to be counterexamples to Hajós’ …

… Hajos abgeleitet hatte und an welche er auf dem Kolloquium erinnerte (siehe z. B. die … Die
oben erwähnten Bedingungen, unter welchen ein Graph ein H-Graph ist, vermehren wir nun …

… , using Ore's version of Hajos' theorem. We also show that a certain weighted sum over the
proper k-colorings of a graph can be computed from its graph polynomial in a simple manner. …

… into restrictions on Haj\'os-type constructions for graphs with … shortdistance"" identifications
on the first Betti number of N(G)… two graph construction algorithms based on different Haj\'os-…

… In general two graphs are involved in binary operation. Hajos construction is one such … So
two graphs with three operations on vertices and edges increases the difficulty in implanting it. …

… isomorphic graphs with different labels as differentgraphs. Accordingly, we define a graph G
… We will showby downward induction on k (1 _< k <_ q- 1) that we can construct the graph G[…

… Hajós’ Conjecture, on the other hand, was verified only for graphs with maximum degree 4
and for planar graphs… In this paper, we verify Gallai’s and Hajós’ Conjectures for graphs with …

… nation and mutation operators from graph theory. The Hajós Join became the recombination
… digraph obtained by Hajós constructions of the complete symmetric digraph on 3 vertices D(…