The converse of Kelly’s lemma and control-classes in graph reconstruction

summary:We prove a converse of the well-known Kelly’s Lemma. This motivates the introduction of the general notions of $\mathcal{K}$-table, $\mathcal{K}$-congruence and control-class

Trees with the same path-table

As a generalization of isomorphisms of graphs, we consider path-congruences, that is maps which preserve the number of paths of any length.We construct families of pairs of non-isomorphic trees with the same path-table

Social reality and narrative form in the fiction of Henry Green

Social Reality and Narrative Form in the Fiction of Henry Green contests the dominant reading of Henry Green's fiction as an abstract, autonomous textual production. My thesis situates Green into a number of literary and socio-historical contexts and argues that doing so challenges a number of prevailing critical orthodoxies. I also argue that Green's fiction is formally constructed through a variety of dislocations, from displacing the centrality of plot, undermining the integrity of character, silencing the narrative voice and questioning the authenticity of the self. To relate social reality to narrative form, each of the four main chapters is dedicated to one of four substantive aspects of material reality: age, class, geography and the body. In the first chapter, I examine Green's relationship to the writing of his generation and to the concepts of age and youth. I argue that Green was deeply ambivalent towards generational belonging or the notion that identity could be supplied through one's generation. My second chapter investigates Green's treatment of social class and positions his Birmingham factory novel, Living, against 1930s theories of proletarian fiction and its canonical texts. My third chapter considers sites of authority both in the external world (geographic space) as well as within the novelistic space. The eclipsing of the narrator and the subsequent translation of the imaginative faculty to the reader is a part of Green's strategy to displace sites of authority. My final chapter looks at Green‘s treatment of the physical body and argues that disability is a central aspect of his novelistic practice. The impossibility of unity and wholeness, therefore, sheds light not only on the physicality of modern man but also on wholeness as a mental and linguistic possibility when the times are 'breaking up.'EThOS - Electronic Theses Online ServiceUniversity of WarwickGBUnited Kingdo

On the edge-reconstruction number of a tree

The edge-reconstruction number ern(G) of a graph G is equal to the minimum number of edge-deleted subgraphs G−e of G which are sufficient to determine G up to isomorphism. Building upon the work of Molina and using results from computer searches by Rivshin and more recent ones which we carried out, we show that, apart from three known exceptions, all bicentroidal trees have edge-reconstruction number equal to 2. We also exhibit the known trees having edge-reconstruction number equal to 3 and we conjecture that the three infinite families of unicentroidal trees which we have found to have edge-reconstruction number equal to 3 are the only ones.peer-reviewe

Sylow's Theorem and the arithmetic of binomial coefficients

We present a result on the existence and the number of subgroups of any given prime-power order containing an arbitrarily fixed subgroup in a finite group (see also [2]). Our proof is an extension of Krull's generalization ([1],1961)of Sylow's theorem, which leads us to consider a new concept (the conditioned binomial coefficient) of independent combinatorial interest

Trees with the same path-table

none2P. Dulio; V. PannoneDulio, Paolo; V., Pannon

The converse of Kelly’s lemma and control-classes in graph reconstruction

summary:We prove a converse of the well-known Kelly’s Lemma. This motivates the introduction of the general notions of $\mathcal{K}$-table, $\mathcal{K}$-congruence and control-class