-Invariant tensors and graphs
We describe a correspondence between -invariant tensors and graphs. We then show how this correspondence accommodates various types of symmetries and orientations.
Gallai and anti-Gallai graphs of a graph
The paper deals with graph operators—the Gallai graphs and the anti-Gallai graphs. We prove the existence of a finite family of forbidden subgraphs for the Gallai graphs and the anti-Gallai graphs to be -free for any finite graph . The case of complement reducible graphs—cographs is discussed in detail. Some relations between the chromatic number, the radius and the diameter of a graph and its Gallai and anti-Gallai graphs are also obtained.
Gallai's innequality for critical graphs of reducible hereditary properties
In this paper Gallai’s inequality on the number of edges in critical graphs is generalized for reducible additive induced-hereditary properties of graphs in the following way. Let (k ≥ 2) be additive induced-hereditary properties, and . Suppose that G is an -critical graph with n vertices and m edges. Then 2m ≥ δn + (δ-2)/(δ²+2δ-2)*n + (2δ)/(δ²+2δ-2) unless = ² or . The generalization of Gallai’s inequality for -choice critical graphs is also presented.
Game chromatic number of Cartesian product graphs.
Game colouring directed graphs.
Game list colouring of graphs.
Game saturation of intersecting families
We consider the following combinatorial game: two players, Fast and Slow, claim k-element subsets of [n] = 1, 2, …, n alternately, one at each turn, so that both players are allowed to pick sets that intersect all previously claimed subsets. The game ends when there does not exist any unclaimed k-subset that meets all already claimed sets. The score of the game is the number of sets claimed by the two players, the aim of Fast is to keep the score as low as possible, while the aim of Slow is to postpone...
Ganzzahlige planare Darstellungen der platonischen Körper.
Gaps and dualities in Heyting categories
We present an algebraic treatment of the correspondence of gaps and dualities in partial ordered classes induced by the morphism structures of certain categories which we call Heyting (such are for instance all cartesian closed categories, but there are other important examples). This allows to extend the results of [14] to a wide range of more general structures. Also, we introduce a notion of combined dualities and discuss the relation of their structure to that of the plain ones.
Gaps in the chromatic spectrum of face-constrained plane graphs.
Gaussian Binomial Coefficients.
GBRDs with block size three over 2-groups, semi-dihedral groups and nilpotent groups.
Gedanken zur Vier-Farben-Vermutung.
Gelfand-Graev characters of the finite unitary groups.
Genealogy of simple permutations with order a power of two.
General bounds for identifying codes in some infinite regular graphs.
General convolutions motivated by designs
General numeration I. Gauged schemes.
The paper deals with special partitions of whole numbers in the following form: given a sequence of pairs {[Gi;Di]} of positive integers in which the Gi form a strictly increasing sequence, sums of the form ∑niGi, with 0 ≤ ni ≤ Di, are considered. The correspondence[nk ... n0] → ∑i≤k niGidefines then a mapping α from a set M of numerals, called Neugebauer symbols, satisfying 0 ≤ ni ≤ Di, into the set W of all non-negative integers. In M, initial zeros are supressed and M is ordered in the usual...
General numeration II. Division schemes.
This is the second in a series of two papers on numeration schemes. Whereas the first paper emphasized grouping as exemplified in the partition of a number so as to obtain its base two numeral, the present paper takes at its point of departure the method of repeated divisions, as in the calculation of the base two numeral for a number by dividing it by two, then dividing the quotient by two, etc., and collecting the remainders. This method is a sort of classification scheme - odd or even.
General properties involving reciprocals of binomial coefficients.