The obstructions for toroidal graphs with no K3,3K_{3,3}'s

Forbidden minors and subdivisions for toroidal graphs are numerous. We consider the toroidal graphs with no $K_{3,3}$-subdivisions that coincide with the toroidal graphs with no $K_{3,3}$-minors. These graphs admit a unique decomposition into planar components and have short lists of obstructions. We provide the complete lists of four forbidden minors and eleven forbidden subdivisions for the toroidal graphs with no $K_{3,3}$'s and prove that the lists are sufficient.Comment: 10 pages, 7 figures, revised version with additional detail

Max Flesch (1852–1943): Veterinäranatom, Arzt und NS-Opfer

The Jewish physician Dr. med. Max Flesch, a student of the Würzburger anatomist Albert von Kölliker (1817–1905), was professor of anatomy, histology and embryology at the School of Veterinary Medicine in Bern from 1882–1887. He was the first at that school who unified the three anatomical fields in one hand. From his Institute came Oskar Rubeli (1861–1952) who was also his successor. From 1888 on Max Flesch was engaged as practitioner and later as gynaecologist. During the First World War he proved his worth as a hospital physician. After the war he most likely was working for another decade in his practice in Frankfurt before retiring in Hochwaldhausen at the Hessian Vogelsberg. During his retirement Flesch published his experiences as l nurse and hospital physician, respectively during the wars 1870/71 and 1914–1918. With the assumption of power by the National Socialists the living conditions for Jews in Germany radically changed; also Max Flesch became victim of the Nazi racism. Although very old he was carried off 1942 into the concentration camp Theresienstadt where he lost his life in May 1943. We owe Max Flesch honourable remembranceDer jüdische Arzt Dr. med. Max Flesch, ein Schüler des Würzburger Anatomen Albert von Koelliker (1817–1905), war von 1882–1887 Professor für Anatomie, Histologie und Embryologie an der Tierarzneischule in Bern. Als solcher vereinigte er erstmals an der Schule die drei anatomischen Sparten in einer Hand. Aus seinem Institut ging Oskar Rubeli (1861–1952) hervor, der auch sein Nachfolger wurde. Ab 1888 engagierte sich Max Flesch als praktizierender Arzt und später als Frauenarzt. Im 1. Weltkrieg bewährte er sich als Lazarettarzt. Nach Kriegsende wirkte er vermutlich noch ein Jahrzehnt in seiner Praxis in Frankfurt, bevor er sich auf seinen Altensitz in Hochwaldhausen im hessischen Vogelsberg zurückzog. Flesch publizierte hier seine Erfahrungen als Krankenpfleger bzw. Lazarettarzt aus den Kriegen 1870/71 und 1914–1918. Mit der Machtübernahme durch die Nationalsozialisten änderten sich die Lebensbedingungen für Juden in Deutschland von Grund auf; auch Max Flesch wurde Opfer des Nationalsozialistischen Rassenwahns. Obwohl hoch betagt, wurde er 1942 in das Konzentrationslager Theresienstadt verschleppt und kam dort im Mai 1943 ums Leben. Wir schulden Max Flesch ein ehrendes Gedenken

COMPUTED TOMOGRAPHIC ANATOMY AND CHARACTERISTICS OF RESPIRATORY ASPERGILLOSIS IN JUVENILE WHOOPING CRANES

Respiratory diseases are a leading cause of morbidity and mortality in captivity reared, endangered whooping cranes (Grus americana). Objectives of this retrospective, case series, cross‐sectional study were to describe computed tomography (CT) respiratory anatomy in a juvenile whooping crane without respiratory disease, compare CT characteristics with gross pathologic characteristics in a group of juvenile whooping cranes with respiratory aspergillosis, and test associations between the number of CT tracheal bends and bird sex and age. A total of 10 juvenile whooping cranes (one control, nine affected) were included. Seven affected cranes had CT characteristics of unilateral extrapulmonary bronchial occlusion or wall thickening, and seven cranes had luminal occlusion of the intrapulmonary primary or secondary bronchi. Air sac membrane thickening was observed in three cranes in the cranial and caudal thoracic air sacs, and air sac diverticulum opacification was observed in four cranes. Necropsy lesions consisted of severe, subacute to chronic, focally extensive granulomatous pathology of the trachea, primary bronchi, lungs, or air sacs. No false positive CT scan results were documented. Seven instances of false negative CT scan results occurred; six of these consisted of subtle, mild air sacculitis including membrane opacification or thickening, or the presence of small plaques found at necropsy. The number of CT tracheal bends was associated with bird age but not sex. Findings supported the use of CT as a diagnostic test for avian species with respiratory disease and tracheal coiling or elongated tracheae where endoscopic evaluation is impractical

A KURATOWSKI THEOREM FOR ORIENTABLE SURFACES

Let $SIGMA$ denote a 2-dimensional surface. A graph $G$ is irreducible for $SIGMA$ provided that $G$ does not embed into $SIGMA$, but every proper subgraph of $G$ does. Let $I$($SIGMA$) denote the set of graphs with vertex degree at least three that are irreducible for $SIGMA$. In this paper we prove that $I$($SIGMA$) is finite for each orientable surface. Together with the result by D. Archdeacon and Huneke, stating that $I$($SIGMA$) is finite for each non-orientable surface, this settles a conjecture of Erd$o dotdot$'s from the 1930s that $I$($SIGMA$) is finite for each surface $SIGMA$. Let $SIGMA sub n$ denote the closed orientable surface of genus $n$. We also write $gamma$($SIGMA$) to denote the genus of orientable surface $SIGMA$. Let $G$ be a finite graph. An embedding of $G$ into a surface $SIGMA$ is a topological map \o'0 /'$:G -> SIGMA$. The orientable genus $gamma$($G$) of the graph $G$ is defined to be the least value of $gamma$($SIGMA$) for all orientable surfaces $SIGMA$ into which $G$ can be embedded. Let $P$ be a property of a graph $G$. We say that $G$ is $P$-critical provided that $G$ has property $P$ but no proper subgraph of $G$ has property $P$. For example, if $P$ is the property that $gamma$($G$) $>= 1$, then the $P$-critical graphs are the two Kuratowski graphs $K sub 5$ and $K sub 3,3$. In general, if $P$ is the property that $gamma$($G$) $>= n$, then a $P$-critical graph can be embedded in $SIGMA sub n$ but not in $SIGMA sub {n - 1}$. Such a $P$-critical graph is also called irreducible for the surface $SIGMA sub {n - 1}$. For any surface $SIGMA$, let $I$($SIGMA$) denote the set of graphs that have no vertices of degree two and are irreducible for $SIGMA$.We are currently acquiring citations for the work deposited into this collection. We recognize the distribution rights of this item may have been assigned to another entity, other than the author(s) of the work.If you can provide the citation for this work or you think you own the distribution rights to this work please contact the Institutional Repository Administrator at [email protected]

ON COMPUTING ALL MINIMAL GRAPHS THAT ARE NOT EMBEDDABLE INTO THE PROJECTIVE PLANEPART 1

No AbstractWe are currently acquiring citations for the work deposited into this collection. We recognize the distribution rights of this item may have been assigned to another entity, other than the author(s) of the work.If you can provide the citation for this work or you think you own the distribution rights to this work please contact the Institutional Repository Administrator at [email protected]

FUNDAMENTAL THEORECTICAL CONCEPTS, SELECTED FOR THE STARTING COMPUTER SCIENTIST

This is a report on the subjects that I have chosen as material for an introductory course to the theory of computer science. I have been teaching such a course for many years and I have tried out many different approaches - the latest one, described here, seems to be the most successful one so far. My main objective has been to introduce the fundamental concepts of Computability and Specification, Implementation and Verification to the student in such a way that the essential heuristic ideas, on which these concepts are based become transparent. It is a nontrivial task to find a good compromise between the amount of formal detail that is needed to describe these concepts properly and between the amount of informal and intuitive argument that is necessary for the student to clearly see the underlying ideas.We are currently acquiring citations for the work deposited into this collection. We recognize the distribution rights of this item may have been assigned to another entity, other than the author(s) of the work.If you can provide the citation for this work or you think you own the distribution rights to this work please contact the Institutional Repository Administrator at [email protected]

ON COMPUTING ALL IRREDUCIBLE NON-EMBEDDABLE GRAPHS FOR THE PROJECTIVE PLANE THAT CONTAIN K sub 3,4

In this paper we compute a complete list of all 3-connected irreducible graphs containing a subgraph contractable to K sub 3,4 that are not embeddable into the projective plane.We are currently acquiring citations for the work deposited into this collection. We recognize the distribution rights of this item may have been assigned to another entity, other than the author(s) of the work.If you can provide the citation for this work or you think you own the distribution rights to this work please contact the Institutional Repository Administrator at [email protected]

PROVING THE COMPLETENESS OF A LIST OF 19 IRREDUCIBLE NON-EMBEDDABLE GRAPHSFOR THE PROJECTIVE PLANE THAT CONTAIN 3,4

In this paper we show that the list A sub 2 , B sub 1 , B sub 7 , C sub 3 , C sub 4 , C sub 7 , D sub 2 , D sub 3 , D sub 9 , D sub 12 , D sub 17 , E sub 2 , E sub 3 , E sub 5, E sub 11 , E sub 18 , E sub 19 , E sub 27 , G is the complete list of all 3-connected irreducible graphs that cannot be embedded into the projective plane and that contain {K sub 3,4} as a minor. The graphs are named as in [1].We are currently acquiring citations for the work deposited into this collection. We recognize the distribution rights of this item may have been assigned to another entity, other than the author(s) of the work.If you can provide the citation for this work or you think you own the distribution rights to this work please contact the Institutional Repository Administrator at [email protected]