【專題演講】Central Star Decomposition in Graphs: Insights and Research
講題：Central Star Decomposition in Graphs: Insights and Research
講者：MARK L. CAAY
(Assistant professor, Department of Mathematics and Statistics, College of Science, Polytechnic University of the Philippines, Manila)
時間：115年10月5日(星期一)上午09：00-10：30
地點：民生校區五育樓401教室
摘要
Graph decomposition plays a central role in structural and extremal combinatorics, bridging abstract graph structures with broader areas in discrete mathematics and theoretical computer science. This presentation is divided into two parts, balancing past research with future mathematical trajectories. In the first half, we review our foundational results on Central Star Decomposition (CSD) – an edge-partitioning scheme into stars centered at distinct vertices. We outline core structural characterizations, including necessary and sufficient criteria derived via Hall’s Marriage Theorem, links to equivalences with directed graph orientations. In the second half, we shift focus to ongoing projects and future research horizons. We explore how central star decompositions connect to other domains of mathematics, including combinatorial representations, dominations, and leavitt path algebra.
講者：MARK L. CAAY
(Assistant professor, Department of Mathematics and Statistics, College of Science, Polytechnic University of the Philippines, Manila)
時間：115年10月5日(星期一)上午09：00-10：30
地點：民生校區五育樓401教室
摘要
Graph decomposition plays a central role in structural and extremal combinatorics, bridging abstract graph structures with broader areas in discrete mathematics and theoretical computer science. This presentation is divided into two parts, balancing past research with future mathematical trajectories. In the first half, we review our foundational results on Central Star Decomposition (CSD) – an edge-partitioning scheme into stars centered at distinct vertices. We outline core structural characterizations, including necessary and sufficient criteria derived via Hall’s Marriage Theorem, links to equivalences with directed graph orientations. In the second half, we shift focus to ongoing projects and future research horizons. We explore how central star decompositions connect to other domains of mathematics, including combinatorial representations, dominations, and leavitt path algebra.
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