The Rule of Law as a Law of Standards: Interpreting the Internal Revenue Code

This Essay seeks to demonstrate that the interpretive use of standards in applying provisions of the Internal Revenue Code is not inconsistent with the rule of law. Part I discusses the relationship between rules and the rule of law and explains why we think so many tax scholars are drawn to a view of the tax law as consisting primarily of rules. We then demonstrate that the definition of income is properly understood as a standard. Part II addresses the descriptive dimension of this claim, summarizing and expanding our previous discussion of the definition of income to determine whether the term is susceptible to construction as a rule. We show that even a brief trip through some of the litigation required to determine whether certain items are income leads to the conclusion that the definition of income is not a rule. Part III addresses the normative dimension of our claim. There, we tease out the functions served by interpreting income as a standard and question where the interpretive authority lies with respect to the Code in order to argue that income ought to be treated as a standard. Part IV turns to several examples of what Professor Lawrence Zelenak regards as either a “disregard” or an “underenforcement” of the law to clarify our understanding of interpretation. We then conclude by observing that the Code does not “read itself”: Deciding whether a provision is itself a rule or a standard is itself an act of interpretation. Moreover, interpreting a provision as a standard is fully consistent with the rule of law

A note on 2--bisections of claw--free cubic graphs

A \emph{$k$--bisection} of a bridgeless cubic graph $G$ is a $2$--colouring of its vertex set such that the colour classes have the same cardinality and all connected components in the two subgraphs induced by the colour classes have order at most $k$. Ban and Linial conjectured that {\em every bridgeless cubic graph admits a $2$--bisection except for the Petersen graph}. In this note, we prove Ban--Linial's conjecture for claw--free cubic graphs

A formulation of a (q+1,8)-cage

Let $q\ge 2$ be a prime power. In this note we present a formulation for obtaining the known $(q+1,8)$-cages which has allowed us to construct small $(k,g)$--graphs for $k=q-1, q$ and $g=7,8$. Furthermore, we also obtain smaller $(q,8)$-graphs for even prime power $q$.Comment: 14 pages, 2 figure