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A graph is even-hole-free if it has no induced even cycles of length 4 or more. A cap is a cycle of length at least 5 with exactly one chord and that chord creates a triangle with the cycle. In this paper, we consider (cap, even hole)-free graphs, and more generally, (cap, 4-hole)-free odd-signable graphs. We give an explicit construction of these graphs. We prove that every such graph G has a vertex of degree at most 3/2ω (G) -1, and hence χ(G)≤3/2ω (G), where ω(G) denotes the size of aarXiv:1611.08066v1 fatcat:we3h6o6bofeldlbzy6ouyaux6y