Elementary Graphs with Respect to f-Parity Factors

Elementary graphs with respect to (1, f)-odd factors

This note concerns the (1, f)-odd subgraph problem, i.e. we are given an undirected graph G and an odd value function f : V (G) → N, and our goal is to find a spanning subgraph F of G with degF ≤ f minimizing the number of even degree vertices. First we prove a Gallai–Edmonds type structure theorem and some other known results on the (1, f)-odd subgraph problem, using an easy reduction to the m...

SPIN AND PARITY DETERMINATION OF ELEMENTARY PARTICLESl

A central problem in the physics of elementary particles concerns the establishment of their quantum numbers. Recent developments in the theoretical classification of particles states have added impetus to this ac­ tivity as a means of making meaningful confrontation between theoretical proposals and experiment. In this review we confine our attention to the in­ ternal quantum numbers of spin a...

Partial Parity (g, f)-Factors and Subgraphs Covering Given Vertex Subsets

Let G be a graph and W a subset of V (G). Let g, f : V (G) → Z be two integer-valued functions such that g(x) ≤ f(x) for all x ∈ V (G) and g(y) ≡ f(y) (mod 2) for all y ∈ W . Then a spanning subgraph F of G is called a partial parity (g, f)-factor with respect to W if g(x) ≤ degF (x) ≤ f(x) for all x ∈ V (G) and degF (y) ≡ f(y) (mod 2) for all y ∈ W . We obtain a criterion for a graph G to have...

A Degree Condition For Graphs to Have Connected (g, f)-Factors

Parity Games on Bounded Phase Multi-pushdown Systems

In this paper we address the problem of solving parity games over the configuration graphs of bounded phase multi-pushdown systems. A non-elementary decision procedure was proposed for this problem by A. Seth. In this paper, we provide a simple and inductive construction to solve this problem. We also prove a non-elementary lower-bound, answering a question posed by A.Seth.