4 citations · 12 across the 17 of their papers we have counts for
18 papers
Adjacent vertex distinguishing total chromatic number of graph products
Amitayu Banerjee, Jayabalan Geetha, Kanagasabapathi Somasundaram
The adjacent vertex distinguishing (AVD)-total chromatic number of a graph is the least integer for which has a proper total coloring with colors s…
AVD Total Colorings of Subdivision Graphs, Joins, and Deleted Lexicographic Products
Amitayu Banerjee
In 2020, Panda, Verma, and Keerti asked whether the central graph of every graph satisfies the AVD-total coloring conjecture. In this paper, we verify the conjecture for central gr…
Automorphism Groups and Structure of 4-Valent Cayley Graphs on Dihedral Groups
Amitayu Banerjee
Let be a finite group and let be an inverse-closed subset of not containing the identity. The Cayley graph has vertex set , where two vertices $x…
The List-distinguishing chromatic number of graphs containing only small complete bigraphs
Amitayu Banerjee
In 2006, Collins and Trenk obtained a general sharp upper bound for the distinguishing chromatic number of a connected graph. Inspired by Catlin's combinatorial techniques from 197…
Automorphism groups and Distinguishing Colorings of Central and Middle Graphs
Amitayu Banerjee, Alexa Gopaulsingh, Zalán Molnár
Let G be a simple, finite, connected, and undirected graph. The middle graph M(G) of G is obtained from the subdivision graph S(G) after joining pairs of subdivided vertices that l…
On the Cost Number of Graphs with Determining Number Two
Alexa Gopaulsingh, Zalán Molnár, Amitayu Banerjee
A distinguishing vertex coloring of a graph is a vertex coloring such that only the identity automorphism of preserves the coloring. A graph is -distinguishable if it ad…
Distinguishing chromatic number of middle and subdivision graphs
Amitayu Banerjee, Alexa Gopaulsingh, Zalán Molnár
Let be a simple finite connected graph of order greater than or equal to . We obtain the following results: (1). We apply a result of Hamada and Yoshimura from 1976 and…
Brooks' type theorems for coloring parameters of locally finite graphs and Konig's Lemma
Amitayu Banerjee, Zalán Molnár, Alexa Gopaulsingh
In the past, analogues to Brooks' theorem have been found for various parameters of graph coloring for infinite locally finite connected graphs in ZFC. We prove these theorems are…
Upper bounds for the list-distinguishing chromatic number
Amitayu Banerjee, Zalán Molnár, Alexa Gopaulsingh
We prove analogs of Brooks' Theorem for the list-distinguishing chromatic number of different classes of simple finite connected graphs. Moreover, we determine two upper bounds for…
On the Rainbow Ramsey theorem and the Canonical Ramsey Theorem for pairs without AC
Amitayu Banerjee, Alexa Gopaulsingh, Zalán Molnár
In set theory without the Axiom of Choice, we study the set-theoretic strength of a generalized version of the Rainbow Ramsey theorem and the Canonical Ramsey Theorem for pairs int…
Distinguishing colorings, proper colorings, and covering properties without the Axiom of Choice
Amitayu Banerjee, Zalán Molnár, Alexa Gopaulsingh
We work with simple graphs in ZF (Zermelo--Fraenkel set theory without the Axiom of Choice (AC)) and assume that the sets of colors can be either well-orderable or non-well-orderab…
On Erdos--Dushnik--Miller theorem without AC
Amitayu Banerjee, Alexa Gopaulsingh
In set theory without the Axiom of Choice, we study the possible placement of Erdos-Dushnik-Miller theorem restricted to an uncountable set of vertices in the hierarchy of weak cho…
Partition models, Permutations of infinite sets without fixed points, and weak forms of AC
Amitayu Banerjee
We study new relations of the following statements with weak choice principles in ZF and ZFA. 1. There does not exist an infinite Hausdorff space X such that every infinite subset…
Maximal independent sets, variants of chain/antichain principle and cofinal subsets without AC
Amitayu Banerjee
In set theory without the Axiom of Choice (AC), we observe new relations of the following statements with weak choice principles. 1. Every locally finite connected graph has a maxi…
On some applications of strongly compact Prikry forcing
Amitayu Banerjee
We work with symmetric inner models of forcing extensions based on strongly compact Prikry forcing to extend some known results.
Chromatic number of the product of graphs, graph homomorphisms, Antichains and cofinal subsets of posets without AC
Amitayu Banerjee, Zalán Gyenis
We have observations concerning the set theoretic strength of the following combinatorial statements without the axiom of choice. 1. If in a partially ordered set, all chains are f…
Combinatorial Properties and Dependent choice in symmetric extensions based on Lévy Collapse
Amitayu Banerjee
We work with symmetric extensions based on Lévy Collapse and extend a few results of Arthur Apter. We prove a conjecture of Ioanna Dimitriou from her P.h.d. thesis. We also observe…
First order logic without equality on relativized semantics
Amitayu Banerjee, Mohamed Khaled
Let be any ordinal. We consider the class of relativized diagonal free set algebras of dimension . With same technique, we prove several important res…