We study equitable allocation of indivisible goods and money among agents with other-regarding preferences. First, we argue that Foley’s (1967) equity test, i.e., the requirement that no agent prefer the allocation obtained by swapping her consumption with another agent, is suitable for our environment. Then, we establish the existence of allocations passing this test for a general domain of pr...

1 Department of Mathematics, University College of Engineering Nagercoil, Anna University of Technology Tirunelveli (Nagercoil Campus), Nagercoil 629 004, Tamil Nadu, India 2 Department of Mathematics, R.V.S College of Engineering and Technology, Coimbatore 641 402, Tamil Nadu, India 3 Department of Mathematics, Sri Shakthi Institute of Engineering and Technology, Coimbatore 641 062, Tamil Nadu...

We confirm the equitable ∆-coloring conjecture for interval graphs and establish the monotonicity of equitable colorability for them. We further obtain results on equitable colorability about square (or Cartesian) and cross (or direct) products of graphs.

A proper vertex coloring of a graph is equitable if the sizes of its color classes differ by at most one. In this paper, we prove that if G is a graph such that for each edge xy ∈ E(G), the sum d(x)+ d(y) of the degrees of its ends is at most 2r + 1, then G has an equitable coloring with r + 1 colors. This extends the Hajnal–Szemerédi Theorem on graphs with maximum degree r and a recent conject...

For several decades, context effects in picture naming and word reading have been extensively investigated. However, researchers have found no agreement on the explanation of the effects. Whereas it has long been assumed that several types of effect reflect competition in word selection (e.g., Levelt, Roelofs, & Meyer, 1999), recently it has been argued that these effects reflect the exclusion ...

An equitable coloring of a graph is a proper vertex coloring such that the sizes of any two color classes differ by at most one. The least positive integer k for which there exists an equitable coloring of a graph G with k colors is said to be the equitable chromatic number of G and is denoted by χ=(G). The least positive integer k such that for any k′ ≥ k there exists an equitable coloring of ...