Separating rank 3 graphs

Separating Shape Graphs

Detailed memory models that expose individual fields are necessary to precisely analyze code that makes use of low-level aspects such as, pointers to fields and untagged unions. Yet, higher-level representations that collect fields into records are often used because they are typically more convenient and efficient in modeling the program heap. In this paper, we present a shape graph representa...

Separating Quantum Communication and Approximate Rank

One of the best lower bound methods for the quantum communication complexity of a function H (with or without shared entanglement) is the logarithm of the approximate rank of the communication matrix of H . This measure is essentially equivalent to the approximate γ2 norm and generalized discrepancy, and subsumes several other lower bounds. All known lower bounds on quantum communication comple...

The Clique-rank of 3-chromatic Perfect Graphs

The clique-rank of a perfect graph G introduced by Fonlupt and Sebö is the linear rank of the incidence matrix of the maximum cliques of G. We study this rank for 3-chromatic perfect graphs. We prove that if, in addition, G is diamond-free, G has two distinct colorations. An immediate consequence is that the Strong Perfect Graph Conjecture holds for diamond-free graphs and for graphs with cliqu...

Rank-perfect and" weakly rank-perfect graphs

Non-separating trees in connected graphs

Let T be any tree of order d ≥ 1. We prove that every connected graph G with minimum degree d contains a subtree T ′ isomorphic to T such that G − V (T ) is connected.