This book gives an elementary treatment of the basic material about graph spectra, both for
ordinary, and Laplace and Seidel spectra. The text progresses systematically, by covering …

We discuss tree width, a new connectivity invariant of graphs defined by Robertson and
Seymour. We present a duality result and a canonical decomposition theorem tied to this …

Graphs are usually represented as geometric objects drawn in the plane, consisting of
nodes and curves connecting them. The main message of this book is that such a …

In 1990, Colin de Verdiere [7](cf.[8]) introduced an interesting new parameter µ (G) for any
undirected graph G. The parameter was motivated by the study of the maximum multiplicity …

For any undirected graph $ G $, let $\mu (G) $ be the graph parameter introduced by Colin
de Verdière. In this paper we show that $\mu (G)\leq 4$ if and only if $ G $ is linklessly …

A graph G=(V, E) is planar, if it can be drawn in the plane so that its edges are Jordan curves
and they intersect only at their endnodes 1. A plane map is a planar graph with a fixed …

Abstract Galluccio, Goddyn, and Hell proved in 2001 that in any minor‐closed class of
graphs, graphs with large enough girth have a homomorphism to any given odd cycle. In this …

For any undirected graph G, let μ (G) be the graph invariant introduced by Colin de Verdière.
In this paper we study the behavior of μ (G) under clique sums of graphs. In particular, we …

Minor-monotone Graph Invariants Page 1 Minor-monotone Graph Invariants Alexander
Schrijver Summary A graph parameter </>(G) is called minor-monotone if </>(H) :::; ef;(G) for …

We study the relationship between unit-distance representations and Lovasz theta number
of graphs, originally established by Lovasz. We derive and prove min-max theorems. This …