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**1 - 3**of**3**### DEAN RICKLES ON EXPLAINING EXISTENCE

"... ABSTRACT: What are the limits of physics ’ explanatory power? Can physics explain everything? In this paper I discuss a somewhat broader question: can physics explain existence itself? I argue that genuinely ultimate explanations—those that really explain everything—involve the most basic and most g ..."

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ABSTRACT: What are the limits of physics ’ explanatory power? Can physics explain everything? In this paper I discuss a somewhat broader question: can physics explain existence itself? I argue that genuinely ultimate explanations—those that really explain everything—involve the most basic and most general elements of logic. Such explanations cannot be done within physics unless physics undergoes a methodology shift more closely aligning itself with mathematics and logic. However, I give reasons for thinking that just such a shift might be in operation. Even a solipsist agrees there is at least one thing!

### Centre for Discrete Mathematics and Theoretical Computer ScienceSearching for Spanning k-Caterpillars and k-Trees

, 2008

"... We consider the problems of finding spanning k-caterpillars and k-trees in graphs. We first show that the problem of whether a graph has a spanning k-caterpillar is NP-complete, for all k ≥ 1. Then we give a linear time algorithm for finding a spanning 1-caterpillar in a graph with treewidth k. Also ..."

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We consider the problems of finding spanning k-caterpillars and k-trees in graphs. We first show that the problem of whether a graph has a spanning k-caterpillar is NP-complete, for all k ≥ 1. Then we give a linear time algorithm for finding a spanning 1-caterpillar in a graph with treewidth k. Also, as a generalized versions of the depth-first search and the breadth-first search algorithms, we introduce the k-tree search (KTS) algorithm and we use it in a heuristic algorithm for finding a large k-caterpillar in a graph. 1