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Recent research on mysticete fossils from the Late Eocene and Oligocene has revolutionised our understanding of the diversity and evolutionary scenarios for early baleen whales. For example, aetiocetids are a possible, though controversial, lineage that bridges the gap between the toothed and baleen-bearing mysticetes, and eomysticetids show a further transitional step towards the baleen-bearing status, with the presence of non-functional dentition in adults. However, information about the origin of crown mysticetes, including the most recent common ancestor of all extant lineages and its descendants, is critical to further understanding the evolution of baleen whales. The phylogenetic positions of the Oligocene Toipahautea, Whakakai, Horopeta, and Mauicetus from New Zealand remain unresolved and problematic, but all four genera show a close relationship with crown mysticetes. The original and subsequent cladistic analyses have consistently revealed a sister relationship between the Toipahautea-to-Mauicetus grade and crown mysticetes, and Horopeta has been placed close to the cetotheriids within the crown group. This review aims to stimulate more research on this topic by elucidating the origin of crown mysticetes, which likely experienced a poorly known radiation event during the Oligocene that established the modern lineages. [ABSTRACT FROM AUTHOR]

Oligocene mysticetes display an unparalleled diversity and morphological disparity in the evolutionary history of Mysticeti. However, their paleoecological aspects, such as the patterns of coexistence of different morphotypes, remain poorly explored. Here we describe an aetiocetid (toothed mysticete) from the Jinnobaru Formation (lower upper Oligocene, about 28 million years ago) of Umashima Island, Kitakyushu, Japan. Our description of a toothed mysticete from the Oligocene of Umashima exemplifies the coexistence of toothed and baleen-assisted mysticetes in the northwestern Pacific. Hopefully, new finds of Oligocene mysticetes will lead to a well-sampled dataset for analyzing this and other related paleoecological traits to understand the demise of "archaic" Oligocene mysticetes and the subsequent rise of the modern-looking baleen-bearing whales in Miocene times. [ABSTRACT FROM AUTHOR]

A t-tone k-coloring of a graph G=(V,E) is a function f:V→[k]t such that |f(u)∩f(v)| for all distinct vertices u and v. The t-tone chromatic number of G, denoted τt(G), is the smallest positive integer k such that G has a t-tone k-coloring. The Wiener index W(G) of a connected graph G is the sum of the distances of all pairs of vertices of G. In this paper, we prove that τt(G)≥t|V|-W(G)+|V|2 for a connected graph G and obtain a characterization when the equality holds. As a result, for each graph G (not necessarily connected), we obtain a formula for the t-tone chromatic number of G when t is sufficiently large. [ABSTRACT FROM AUTHOR]