13 citations · 39 across the 22 of their papers we have counts for
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Acyclic Edge Coloring of 3-sparse Graphs
Nevil Anto, Manu Basavaraju, Shashanka Kulamarva
A proper edge coloring of a graph without any bichromatic cycles is said to be an acyclic edge coloring of the graph. The acyclic chromatic index of a graph denoted by ,…
Upper Bounds on the Acyclic Chromatic Index of Degenerate Graphs
Nevil Anto, Manu Basavaraju, Suresh Manjanath Hegde +1
An acyclic edge coloring of a graph is a proper edge coloring without any bichromatic cycles. The acyclic chromatic index of a graph denoted by , is the minimum such…
Acyclic Chromatic Index of Chordless Graphs
Manu Basavaraju, Suresh Manjanath Hegde, Shashanka Kulamarva
An acyclic edge coloring of a graph is a proper edge coloring in which there are no bichromatic cycles. The acyclic chromatic index of a graph denoted by , is the minimu…
Gallai's Path Decomposition for 2-degenerate Graphs
Nevil Anto, Manu Basavaraju
Gallai's path decomposition conjecture states that if is a connected graph on vertices, then the edges of can be decomposed into at most pa…
Variants of the Gyàrfàs-Sumner Conjecture: Oriented Trees and Rainbow Paths
Manu Basavaraju, L. Sunil Chandran, Mathew C. Francis +1
Given a finite family of graphs, we say that a graph is "-free" if does not contain any graph in as a subgraph. A vertex-colored gr…
Weakening Total Coloring Conjecture: Weak TCC and Hadwiger's Conjecture on Total Graphs
Manu Basavaraju, L. Sunil Chandran, Mathew C. Francis +1
Hadwiger's conjecture is one of the most important and long-standing conjectures in graph theory. Reed and Seymour showed in 2004 that Hadwiger's conjecture is true for line graphs…
The linear arboricity conjecture for graphs of low degeneracy
Manu Basavaraju, Arijit Bishnu, Mathew Francis +1
A linear forest is an acyclic graph whose each connected component is a path; or in other words, it is an acyclic graph whose maximum degree is at most 2. A linear coloring of a gr…
On Induced Colourful Paths in Triangle-free Graphs
Jasine Babu, Manu Basavaraju, L. Sunil Chandran +1
Given a graph whose vertices have been properly coloured, we say that a path in is "colourful" if no two vertices in the path have the same colour. It is a corollary…
Separation dimension of bounded degree graphs
Noga Alon, Manu Basavaraju, L. Sunil Chandran +2
The 'separation dimension' of a graph is the smallest natural number for which the vertices of can be embedded in such that any pair of disjoint edges in…
Boxicity and separation dimension
Manu Basavaraju, L. Sunil Chandran, Martin Charles Golumbic +2
A family of permutations of the vertices of a hypergraph is called 'pairwise suitable' for if, for every pair of disjoint edges in , there exists a permuta…
Separation dimension of sparse graphs
Manu Basavaraju, L. Sunil Chandran, Rogers Mathew +1
The separation dimension of a graph is the smallest natural number for which the vertices of can be embedded in such that any pair of disjoint edges in $…
Maximal induced matchings in triangle-free graphs
Manu Basavaraju, Pinar Heggernes, Pim van 't Hof +2
An induced matching in a graph is a set of edges whose endpoints induce a -regular subgraph. It is known that any -vertex graph has at most maxima…
Strong chromatic index of chordless graphs
Manu Basavaraju, Mathew C. Francis
A strong edge colouring of a graph is an assignment of colours to the edges of the graph such that for every colour, the set of edges that are given that colour form an induced mat…
Pairwise Suitable Family of Permutations and Boxicity
Manu Basavaraju, L. Sunil Chandran, Rogers Mathew +1
A family F of permutations of the vertices of a hypergraph H is called "pairwise suitable" for H if, for every pair of disjoint edges in H, there exists a permutation in F in which…
Rainbow Connection Number of Graph Power and Graph Products
Manu Basavaraju, L. Sunil Chandran, Deepak Rajendraprasad +1
Rainbow connection number, rc(G), of a connected graph G is the minimum number of colors needed to color its edges so that every pair of vertices is connected by at least one path…
Rainbow Connection Number and Radius
Manu Basavaraju, L. Sunil Chandran, Deepak Rajendraprasad +1
The rainbow connection number, rc(G), of a connected graph G is the minimum number of colours needed to colour its edges, so that every pair of its vertices is connected by at leas…
-Regular graphs of acyclic chromatic index at least
Manu Basavaraju, L. Sunil Chandran, Manoj Kummini
An edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The \emph{acyclic chromatic index} of a graph is the minimum number k suc…
Acyclic Edge colorings of 2-degenerate graphs
Manu Basavaraju, L. Sunil Chandran
An edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycle s. The \emph{acyclic chromatic index} of a graph is the minimum number k su…
Acyclic Edge Coloring of Graphs with Maximum Degree 4
Manu Basavaraju, L. Sunil Chandran
An edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycle s. The \emph{acyclic chromatic index} of a graph is the minimum number k su…