Path-factors involving paths of order seven and nine

In this paper, we show the following two theorems (here $c_{i}(G-X)$ is the number of components $C$ of $G-X$ with $|V(C)|=i$): (i)~If a graph $G$ satisfies $c_{1}(G-X)+\frac{1}{3}c_{3}(G-X)+\frac{1}{3}c_{5}(G-X)\leq \frac{2}{3}|X|$ for all $X\subseteq V(G)$, then $G$ has a $\{P_{2},P_{7}\}$-factor. (ii)~If a graph $G$ satisfies $c_{1}(G-X)+c_{3}(G-X)+\frac{2}{3}c_{5}(G-X)+\frac{1}{3}c_{7}(G-X)\leq \frac{2}{3}|X|$ for all $X\subseteq V(G)$, then $G$ has a $\{P_{2},P_{9}\}$-factor.Comment: 29 pages, 4 figure

Edges not contained in triangles and the distribution of contractible edges in a 4-connected graph

AbstractWe prove results concerning the distribution of 4-contractible edges in a 4-connected graph G in connection with the edges of G not contained in a triangle. As a corollary, we show that if G is 4-regular 4-connected graph, then the number of 4-contractible edges of G is at least one half of the number of edges of G not contained in a triangle

Path factors in claw-free graphs

AbstractA graph G is called claw-free if G has no induced subgraph isomorphic to K1,3. We prove that if G is a claw-free graph with minimum degree at least d, then G has a path factor such that the order of each path is at least d+1

Cultural trauma, counter-narratives, and dialogical intellectuals: the works of Murakami Haruki and Mori Tatsuya in the context of the Aum affair

In this article, we offer a new conceptualization of intellectuals as carriers of cultural trauma through a case study of the Aum Affair, a series of crimes and terrorist attacks committed by the Japanese new religious movement Aum Shinrikyō. In understanding the performative roles intellectuals play in trauma construction, we offer a new dichotomy between “authoritative intellectuals,” who draw on their privileged parcours and status to impose a distinct trauma narrative, and “dialogical intellectuals,” who engage with local actors dialogically to produce polyphonic and open-ended trauma narratives. We identify three dimensions of dialogical intellectual action: firstly, the intellectuals may be involved in dialogue with local participants; secondly, the intellectual products themselves may be dialogical in content; and thirdly, there might be a concerted effort on the part of the intellectuals to record and to disseminate dialogue between local participants. In the context of the Aum Affair, we analyze the works of Murakami Haruki and Mori Tatsuya as dialogical intellectuals while they sought, with the help of local actors’ experiences, to challenge and to alter the orthodox trauma narrative of Aum Shinrikyō as exclusively a social evil external to Japanese society and an enemy to be excluded from it. Towards the end of the article, we discuss the broader significance of this case study and suggest that in light of recent societal and technological developments, the role and scope of dialogical intellectuals as carriers of trauma are changing and possibly expanding