Italo Jose Dejter (December 17, 1939) is an Argentine-born American mathematician, a retired professor of mathematics and computer science from the University of Puerto Rico, (August 1984-February 2018) and a researcher in algebraic topology, differential topology, graph theory, coding theory and combinatorial designs.

He was a professor at the Federal University of Santa Catarina, Brazil, from 1977 to 1984, with grants from the National Council for Scientific and Technological Development, (CNPq).

The sections below describe the relevance of Dejter's work in the research areas mentioned in the first paragraph above, or in the adjacent box.

Petrie[2] also asked: What are necessary and sufficient conditions for the existence of a smooth G-map properly G-homotopic to F and transverse to the zero-section?

[48] and by M. Buck and D. Wiedemann in 1984,[49] (though Béla Bollobás presented it to Dejter as a Paul Erdős' conjecture in Jan. 1983) and established by T. Mütze[50] in 2014.

That technique was used by Dejter et al.[51][52][53][54][55][56] In 2014, Dejter[57] returned to this problem and established a canonical ordering of the vertices in a quotient graph (of each middle-levels graph under the action of a dihedral group) in one-to-one correspondence with an initial section of a system of numeration (present as sequence A239903 in the On-Line Encyclopedia of Integer Sequences by Neil Sloane) [58] composed by restricted growth strings[59][60] (with the k-th Catalan number[61] expressed by means of the string 10...0 with k "zeros" and a single "one", as J. Arndt does in page 325 [60]) and related to Kierstead-Trotter lexical matching colors.

1, then the graph generated by the generalized chessknight moves of type (1,2k) on the 2n x 2n-chessboard has Hamilton cycles invariant under quarter turns.

In 1991, Dejter and Neumann-Lara[66] showed that given a group Zn acting freely on a graph G, the notion of a voltage graph[67] is applied to the search for Hamilton cycles in G invariant under an action of Zn on G. As an application, for n = 2 and 4, equivalent conditions and lower bounds for chessknight Hamilton cycles containing paths spanning square quadrants and rectangular half-boards were found, respectively.

The result of (a) above is immediately extended to perfect dominating sets in cubes of dimensions which are powers of 2 whose components contain each an only edge in half the coordinate direction.

On the other hand, in 1991, Dejter and Phelps[70] extended the result of (b) above again to cubes whose dimensions are powers of 2, with components composed each by a unique edge in all coordinate directions.

The Weichsel conjecture[69] was answered in the affirmative by Östergård and Weakley,[71] who found a perfect dominating set in the 13-cube whose components are 26 4-cubes and 288 isolated vertices.

This tool was used to construct infinite families of E-chains of Cayley graphs generated by transposition trees of diameter 2 on symmetric groups.

[75] In contrast, Dejter and O. Tomaiconza[76] showed that there is no efficient dominating set in any Cayley graph generated by a transposition tree of diameter 3.

In 2009,[79] Dejter defined a vertex subset S of a graph G as a quasiperfect dominating set in G if each vertex v of G not in S is adjacent to dv ∈{1,2} vertices of S, and then investigated perfect and quasiperfect dominating sets in the regular tessellation graph of Schläfli symbol {3,6} and in its toroidal quotient graphs, yielding the classification of their perfect dominating sets and most of their quasiperfect dominating sets S with induced components of the form Kν, where ν ∈{1,2,3} depends only on S. Invariants of perfect error-correcting codes were addressed by Dejter in,[80][81] and Dejter and Delgado[82] in which it is shown that a perfect 1-error-correcting code C is 'foldable' over its kernel via the Steiner triple systems associated to its codewords.

Extending the algorithm to infinite-grid graphs of width m-1, periodicity makes the binary decision tree prunable into a finite threaded tree, a closed walk of which yields all such sets S. The graphs induced by the complements of such sets S can be codified by arrays of ordered pairs of positive integers, for the growth and determination of which a speedier algorithm exists.

A recent characterization of grid graphs having total perfect codes S (i.e. with just 1-cubes as induced components, also called 1-PDDS[87] and DPL(2,4)[89]), due to Klostermeyer and Goldwasser,[91] allowed Dejter and Delgado[90] to show that these sets S are restrictions of only one total perfect code S1 in the planar integer lattice graph, with the extra-bonus that the complement of S1 yields an aperiodic tiling, like the Penrose tiling.

In contrast, the parallel, horizontal, total perfect codes in the planar integer lattice graph are in 1-1 correspondence with the doubly infinite {0,1}-sequences.

In 2012, Araujo and Dejter[93] made a conjecturing contribution to the classification of lattice-like total perfect codes in n-dimensional integer lattices via pairs (G,F) formed by abelian groups G and homomorphisms F from Zn onto G, in the line of the Araujo-Dejter-Horak work cited above.

[87] Since 1994, Dejter intervened in several projects in Combinatorial Designs initially suggested by Alexander Rosa, C. C. Lindner and C. A. Rodger and also worked upon with E. Mendelsohn, F. Franek, D. Pike, P. A. Adams, E. J. Billington, D. G. Hoffman, M. Meszka and others, which produced results in the following subjects: Invariants for 2-factorization and cycle systems,[94] Triangles in 2-factorizations,[95][96] Number of 4-cycles in 2-factorizations of complete graphs,[97] Directed almost resolvable Hamilton-Waterloo problem,[98] Number of 4-cycles in 2-factorizations of K2n minus a 1-factor,[99] Almost resolvable 4-cycle systems,[100] Critical sets for the completion of Latin squares[101] Almost resolvable maximum packings of complete graphs with 4-cycles.