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A vertex dominating path in a graph is a path P such that every vertex outside P has a neighbor on P. In 1988 H. Broersma [5] stated a result implying that every n‐vertex k‐connected graph G such that σ(k+2)(G)≥n−2k−1 contains a vertex dominating path. We provide a short, self‐contained proof of this result and further show that every n‐vertex k‐connected graph such that σ2(G)≥2nk+2+f(k) contains a vertex dominating path of length at most (20k)|T|, where T is a minimum dominating set of vertices. An immediate corollary of this result is that every such graph contains a vertex dominating path with length bounded above by a logarithmic function of the order of the graph. To derive this result, we prove that every n‐vertex k‐connected graph with σ2(G)≥2nk+2+f(k) contains a path of length at most 20k|T|, through any set of T vertices where |T|≤n/900k4. [ABSTRACT FROM AUTHOR]

A dominating path in a graph is a path P such that every vertex outside P has a neighbor on P. A result of Broersma from 1988 implies that if G is an n-vertex k-connected graph and [ABSTRACT FROM AUTHOR]

Let X, Y be connected graphs. A graph G is [ABSTRACT FROM AUTHOR]

Building on research theorizing scale, this article proposes augmentations to existing frameworks that will help illuminate how localities are linked to 'stranger collectives' like nations, ethnicities, and global religious 'communities'. In this case of ethnic revival from Mexico's Sierra Mazateca, people use new vernacular literacy practices tied to local musical performances as a way of 'customizing' modular forms deployed by national and global institutions to manage indigenous difference. People 're-imagine' locality through a localized indigenous literacy that takes templates provided by the Mexican state and the Catholic Church and places them in productive tension with local context: musical properties of the indigenous language Mazatec, locally valued performance practices, and local musical-linguistic ideologies. While this revival movement draws on immanently modular forms, once locally embedded they become 'unpiratable', and constitute a new resource for inscribing local belonging. This case suggests the importance of considering linguistic and musical aspects of social context often taken for granted in anthropological investigations of scale. [ABSTRACT FROM AUTHOR]

Though linguistic anthropologists have long surpassed Austin's initial formulation, the performativity concept remains of enduring interest for its utility in exploring how language constitutes social action. I build on those conversations by considering the concept's applicability to a key document used in the conquest of the Americas, an event involving one of the greatest discursive divides in human history. After examining the text's internal structure and what we know of its use, I suggest that the complex performative dynamics at work in the text are tied to the ways it presupposes and simultaneously instantiates social hierarchies by establishing participant roles. Competing interpretations of those participant roles are made possible by the text's strategic indeterminacy and the temporal dynamics of its circulation. I conclude by considering parallels to other texts and speech acts likewise designed to grapple with discursive difference. [ABSTRACT FROM AUTHOR]

For d ≥ 1 and m ≥ 1, a graph has property P d, m if there exist at least m vertex-disjoint paths of length at most d between each pair of vertices. Property P d, m, which has a strong connection to wide diameter, is one way of measuring the reliability of a network. In this article, we first examine the relationship of P d, m to other similar properties and then we prove several results regarding the extremal number for property P d, m (the minimum number of edges needed for a graph to have the property). In particular, we find (i) the extremal number for graphs of certain orders when d = 2, (ii) several extremal graphs when d ≥ 3, (iii) a new lower bound on the extremal number when d ≥ 3, m ≥ 3, and (iv) a new upper bound on the extremal number when d, m are even with d = 4 k + 2( k ≥ 1) and m ≥ 4. © 2012 Wiley Periodicals, Inc. NETWORKS, 2012 [ABSTRACT FROM AUTHOR]

Loosely following the structure of the U.S. election cycle, I identify some of the more important institutions and events that have recently served as venues for field-building scholarly practices and processes in linguistic anthropology. I examine various trends and concerns animating recent publications on language and social life. I discuss the ongoing impact on the field of recent major works that attempt to codify methodological and theoretical approaches to the intersection of language and society. I also consider some of linguistic anthropology's emergent ventures, including new collaborative projects and new proposals for interdisciplinary work. Finally, I discuss some of the political implications of academic specialization, disciplinary boundaries, and impending “generational shift,” both in the subdiscipline and the academy generally. I close by raising questions about future directions and possibilities for research in linguistic anthropology and other interdisciplinary enterprises. [Keywords: linguistic anthropology, interdisciplinarity, linguistic ideology, semiotic practices, linguistic variation] [ABSTRACT FROM AUTHOR]