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Large language model-driven multi-agent systems enhance the reliability of complex reasoning tasks through multi-round deliberation, role specialization, and cross-validation. However, existing multi-agent debate and collaboration frameworks typically adopt fully connected communication, causing the number of messages, token costs, and end-to-end latency to grow approximately quadratically with the number of agents; although fixed sparse topologies reduce overhead, they cannot adapt communication relationships to different task instances or intermediate reasoning states, making them prone either to preserving low-value interactions or to losing critical error-correction information. To address this problem, this paper proposes DySCo (Dynamic Sparse Consensus), a dynamic trust-aware sparse consensus mechanism. In each round of reasoning, DySCo estimates the value of communication edges based on agent reliability, answer divergence, and task relevance, and selects a small number of high-value edges for message exchange under budget constraints; it then aggregates the answers of different agents through dynamic trust weights and terminates the discussion early once consensus stabilizes. This mechanism replaces universal broadcasting with on-demand communication, thereby reducing communication overhead while preserving essential cross-validation information. We further present analyses of communication complexity and consensus stability, and evaluate the performance of DySCo on mathematical reasoning, logical reasoning, and factual question-answering tasks.