The Hall number, the Hall index, and the total Hall number of a graph

The relationship between the distinguishing number and the distinguishing index with detection number of a graph

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Progress on the Hall-Number-Two problem

The graphs with Hall number at most 2 form a class of graphs within which the chromatic number equals the choice (list-chromatic) number. This class has a forbidden-induced-subgraph characterization which has not yet been found, although a fairly imposing collection of minimal forbidden induced subgraphs has been assembled. In this paper we add to the collection, most notably adding (i) K5 with...

Characterization of graphs with hall number 2

Hall’s condition is a simple condition that a graph G and list assignment L must satisfy if G has a proper L-colouring. The Hall number of G is the smallest integer m such that whenever each list has size m and Hall’s condition is satisfied a proper L-colouring exists. Hilton and P.D. Johnson introduced the parameter and showed that a graph has Hall number 1 if and only if every block is a cliq...

اثر هال (hall effect)

the investigation of the relationship between type a and type b personalities and quality of translation

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